%use A09 instead
@misc{A03,
author="Dan Archdeacon",
title="Problems in Topological Graph Theory",
note="{\ttfamily http://\linebreak[0]www\linebreak[0].emba\linebreak[0].uvm.edu/\linebreak[0]$\sim$archdeac/\linebreak[0]problems/\linebreak[0]altcross.html} (accessed April 7th, 2005)",
}

@incollection {KR07,
    AUTHOR = {Kawarabayashi, Ken-ichi and Reed, Bruce},
     TITLE = {Computing crossing number in linear time},
 BOOKTITLE = {S{TOC}'07---{P}roceedings of the 39th {A}nnual {ACM}
              {S}ymposium on {T}heory of {C}omputing},
     PAGES = {382--390},
 PUBLISHER = {ACM},
   ADDRESS = {New York},
      YEAR = {2007},
}

@phdthesis{C08,
    author = "{\v C}ern{\'y}, Jakub",
    title = "Combinatorial and Computational Geometry",
    school ="Charles University",
    year = "2008",
    address = "Prague",
}

@unpublished{BPR?,
author = {Buzaglo, Sarit and Pinchasi, Rom and Rote, G\"{u}nter},
title = "Topological Hyper-Graphs",
year = "2007",
note = "Unpublished manuscript",
}

@article {CN00,
    AUTHOR = {Cairns, Grant and Nikolayevsky, Yury},
     TITLE = {Bounds for generalized thrackles},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {23},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {191--206},
}

%don't use
@unpublished{CN?,
    AUTHOR = {Cairns, Grant and Nikolayevsky, Yury},
     TITLE = {Generalized Thrackles Drawings of Non-Bipartite Graphs},
    note="Preprint, {\ttfamily http://\linebreak[0]www\linebreak[0].latrobe\linebreak[0].edu\linebreak[0].au/\linebreak[0]mathstats%
           /\linebreak[0]staff/\linebreak[0]cairns/\linebreak[0]dvi/\linebreak[0]generalized.pdf}"
}

@article{CN09,
 author = {Grant Cairns and Yury Nikolayevsky},
 title = {Generalized Thrackle Drawings of Non-bipartite Graphs},
 journal = {Discrete Comput. Geom.},
 FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
 volume = {41},
 number = {1},
 year = {2009},
 issn = {0179-5376},
 pages = {119--134},
 doi = {http://dx.doi.org/10.1007/s00454-008-9095-5},
 publisher = {Springer-Verlag New York, Inc.},
 address = {Secaucus, NJ, USA},
 }



@Article{KM91,
  author =       "Jan Kratochv\'{\i}l and Ji\v{r}\'{\i} Matou{\v{s}}ek",
  title =        "String Graphs Requiring Exponential Representations",
  journal =      "Journal of Combinatorial Theory, Series B",
  volume =       "53",
  pages = "1--4",
  year =         "1991"
}


@misc{W?,
author="Douglas West",
title="Open Problems - Graph Theory and Combinatorics",
note="{\ttfamily http://\linebreak[0]www.math\linebreak[0].uiuc\linebreak[0].edu/\linebreak[0]$\sim$west/\linebreak[0]openp/}
(accessed April 7th, 2005)",
}

@book{BMP05,
author = "Peter Brass and William Moser and J\'{a}nos Pach",
title = "Research Problems in Discrete Geometry",
publisher = "Springer",
address = "New York",
year = "2005"}

@BOOK{D97,
author = "Reinhard Diestel",
title = "{Graph Theory}",
publisher = "Springer",
address = "New York",
year = "1997"}

@BOOK{D05,
AUTHOR = {Diestel, Reinhard},
     TITLE = {Graph theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {173},
   EDITION = {Third},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2005},
}

@book {D11,
    AUTHOR = {Diestel, Reinhard},
     TITLE = {Graph theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {173},
   EDITION = {Fourth},
 PUBLISHER = {Springer},
   ADDRESS = {Heidelberg},
      YEAR = {2010},
     PAGES = {xviii+437},
      ISBN = {978-3-642-14278-9},
}

@BOOK{HU79,
author = "Hopcroft, John E. and Ullman, Jeffrey D.",
title = "Introduction to automata theory, languages, and computation",
publisher = "Addison-Wesley",
year = "1979"}

@BOOK{T95,
author = "Tricot, Claude",
title="Curves and Fractal Dimension",
publisher="Springer",
year = "1995"}


@Article{FT91,
    author = "B. Farb and B. Thurston",
    title = "Homeomorphisms and simple closed curves",
    journal = "unpublished manuscript",
    year = "1991"
}

@book {GJ79,
    AUTHOR = {Garey, Michael R. and Johnson, David S.},
     TITLE = {Computers and intractability},
      NOTE = {A guide to the theory of NP-completeness,
              A Series of Books in the Mathematical Sciences},
 PUBLISHER = {W. H. Freeman and Co.},
   ADDRESS = {San Francisco, Calif.},
      YEAR = {1979},
     PAGES = {x+338},
      ISBN = {0-7167-1045-5},
}


@Article{GJ83,
  author =       "Michael R. Garey and David S. Johnson",
  title =        "Crossing number is {NP}-complete",
  journal =      "SIAM Journal on Algebraic and Discrete Methods",
  volume =       "4",
  number =       "3",
  pages =        "312--316",
  year =         "1983",
  ISSN =         "0196-5212"
}

@inProceedings{G76,
  author = "Ron L.~Graham",
  title = "Problem~1",
  booktitle = "Open Problems at 5th Hungarian Colloquium on Combinatorics",
  place = "Keszthely",
  year = "1976"
}

@InProceedings{HLP97,
  author =       "Joel Hass and Jeffrey C. Lagarias and Nicholas Pippenger",
  title =        "The Computational Complexity of Knot and Link
                 Problems",
  pages =        "172--181",
  booktitle =    "Proceedings of the 38th Annual Symposium on
                 Foundations of Computer Science ({FOCS}-97)",
  month =        oct # "~20--22",
  publisher =    "IEEE Computer Society Press",
  address =      "Los Alamitos",
  year =         "1997",
}

@article {HS85,
    AUTHOR = {Hass, Joel and Scott, Peter},
     TITLE = {Intersections of curves on surfaces},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {51},
      YEAR = {1985},
    NUMBER = {1-2},
     PAGES = {90--120},
}

@InProceedings{G01,
    author= "Martin Grohe",
    title = "Computing Crossing Numbers in Quadratic Time",
    pages = "231--236",
    booktitle = "Proceedings of the 32nd ACM Symposium on Theory of Computing",
    month = "july" # "~6--8",
    year = "2001"
}

@book{GT01,
    AUTHOR = {Gross, Jonathan L. and Tucker, Thomas W.},
     TITLE = {Topological graph theory},
      NOTE = {Reprint of the 1987 original.},
 PUBLISHER = {Dover Publications Inc.},
   ADDRESS = {Mineola, NY},
      YEAR = {2001},
     PAGES = {xvi+361},
}

@book{M03,
    AUTHOR = {Matou{\v{s}}ek, Ji{\v{r}}{\'{\i}}},
     TITLE = {Using the {B}orsuk-{U}lam theorem},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2003},
     PAGES = {xii+196},
      ISBN = {3-540-00362-2},
}



@article {KM04,
    AUTHOR = {Kolman, Petr and Matou{\v{s}}ek, Ji{\v{r}}{\'\i}},
     TITLE = {Crossing number, pair-crossing number, and expansion},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {92},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {99--113},
}

@misc{K05,
  author =       "Jan Kratochv\'{\i}l",
  title =        "Geometric representations of graphs",
  note = "Lecture Notes",
  year =         "2005",
}

@incollection {PT05,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Disjoint edges in topological graphs},
 BOOKTITLE = {Combinatorial geometry and graph theory},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {3330},
     PAGES = {133--140},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2005},
}


@book {PS09,
    AUTHOR = {Pach, J{\'a}nos and Sharir, Micha},
     TITLE = {Combinatorial geometry and its algorithmic applications: {The Alcal{\'a} lectures}},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {152},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2009},
     PAGES = {viii+235},
      ISBN = {978-0-8218-4691-9},
}

@article{BD09,
title = "MacLane's theorem for arbitrary surfaces",
journal = "Journal of Combinatorial Theory, Series B",
volume = "99",
number = "2",
pages = "275 - 286",
year = "2009",
note = "",
issn = "0095-8956",
doi = "DOI: 10.1016/j.jctb.2008.03.005",
url = "http://www.sciencedirect.com/science/article/B6WHT-4SC5PHG-1/2/72ac2046283702893f7cfc62a720a9a2",
author = "Henning Bruhn and Reinhard Diestel",
}


@Article{K98,
  author =       "Jan Kratochv\'{\i}l",
  title =        "Crossing Number of Abstract Topological Graphs",
  journal =      "Lecture Notes in Computer Science",
  volume =       "1547",
  pages =        "238--245",
  year =         "1998",
  coden =        "LNCSD9",
  ISSN =         "0302-9743"
}

@incollection{PR04,
    AUTHOR = {Pinchasi, Rom and Radoi{\v{c}}i{\'c}, Rado{\v{s}}},
     TITLE = {Topological graphs with no self-intersecting cycle of length
              4},
 BOOKTITLE = {Towards a theory of geometric graphs},
    SERIES = {Contemp. Math.},
    VOLUME = {342},
     PAGES = {233--243},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
}

@article{PPTT04,
    AUTHOR = {Pach, J{\'a}nos and Pinchasi, Rom and Tardos, G{\'a}bor and
              T{\'o}th, G{\'e}za},
     TITLE = {Geometric graphs with no self-intersecting path of length
              three},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {25},
      YEAR = {2004},
    NUMBER = {6},
     PAGES = {793--811},
      ISSN = {0195-6698},
}



@book {M98,
    AUTHOR = {Menger, Karl},
     TITLE = {Ergebnisse eines mathematischen {K}olloquiums},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Vienna},
      YEAR = {1998},
     PAGES = {x+470},
      ISBN = {3-211-83104-5},
}



@misc{T?,
    AUTHOR = {T{\'o}th, G{\'e}za},
     TITLE = {Note on the pair-crossing number and the odd-crossing number},
   note = "Unpublished manuscript.",
}

@misc{T10,
    AUTHOR = {T{\'o}th, G{\'e}za},
     TITLE = {A better bound for the pair-crossing number},
   note = "Presentation at the {\em Conference on Geoemtric Graph Theory}, Lausanne, Switzerland, 2010.",
}

@misc{T10a,
    AUTHOR = {T{\'o}th, G{\'e}za},
   howpublished  = "Personal communication.",
   year = "2010",
}


@InProceedings{SS01,
  author =       "Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Decidability of String Graphs",
  pages =        "241--246",
  booktitle =    "Proceedings of the 33th Annual {ACM} Symposium on
                 Theory of Computing ({STOC}-2001)",
  year =         "2001",
}

@article {SS05,
    AUTHOR = {Schaefer, Marcus and {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Decidability of string graphs},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {68},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {319--334},
}

@article{PSS09c,
author = {Michael J. Pelsmajer and Marcus Schaefer and Despina Stasi},
title = {Strong {H}anani--{T}utte on the Projective Plane},
publisher = {SIAM},
year = {2009},
journal = {SIAM Journal on Discrete Mathematics},
volume = {23},
number = {3},
pages = {1317-1323},
keywords = {HananiTutte theorem; projective plane; crossing number; independent odd crossing number},
url = {http://link.aip.org/link/?SJD/23/1317/1},
doi = {10.1137/08072485X}
}

@article {AFM17,
    AUTHOR = {\'{A}brego, Bernardo M. and Fern\'{a}ndez-Merchant, Silvia},
     TITLE = {The rectilinear local crossing number of {$K_n$}},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {151},
      YEAR = {2017},
     PAGES = {131--145},
      ISSN = {0097-3165},
   MRCLASS = {05C62 (05C10)},
  MRNUMBER = {3663492},
       DOI = {10.1016/j.jcta.2017.04.003},
       URL = {http://dx.doi.org/10.1016/j.jcta.2017.04.003},
}

@InProceedings{SSS08,
  title =	"Computing {D}ehn Twists and Geometric Intersection
		 Numbers in Polynomial Time",
  author =	"Marcus Schaefer and Eric Sedgwick and Daniel
		 \v{S}tefankovi\v{c}",
  year = 	"2008",
  booktitle =	"Proceedings of the 20th Canadian Conference on Computational Geometry",
  pages = "111-114",
}


@InProceedings{SSS02,
  author =       "Marcus Schaefer and Eric Sedgwick and Daniel {\v S}tefankovi{\v c}",
  title =        "Recognizing String Graphs in {NP}",
  booktitle =    "Proceedings of the 33th Annual {ACM} Symposium on
                 Theory of Computing ({STOC}-2002)",
  year =         "2002",
}

@article {SSS03,
    AUTHOR = {Schaefer, Marcus and Sedgwick, Eric and
              {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Recognizing string graphs in {NP}},
      NOTE = {Special issue on STOC2002 (Montreal, QC)},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {67},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {365--380},
}


@InProceedings{PSS05a,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Removing Even Crossings",
   editor = {Stefan Felsner},
   booktitle = {2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
  pages = "105--109",
  year = "2005",
  series = {DMTCS Proceedings},
  publisher = {Discrete Mathematics and Theoretical Computer Science},
 volume = {AE},
  month="April",
}

@InProceedings{PSS07a,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Removing Even Crossings on Surfaces",
   editor = {Alberto M\'{a}rquez, Jarik Ne\v{s}et\v{r}il and Oriol Serra},
   booktitle = {European Conference on Combinatorics, Graph Theory and Applications (EuroComb '07)},
  pages = "85--90",
  year = "2007",
  series = {Electronic Notes in Discrete Mathematics},
  publisher = {Elsevier},
  month="August",
}


@article {PP08,
    AUTHOR = {Perlstein, Amitai and Pinchasi, Rom},
     TITLE = {Generalized thrackles and geometric graphs in {$\RN^3$}
              with no pair of strongly avoiding edges},
   JOURNAL = {Graphs Combin.},
  FJOURNAL = {Graphs and Combinatorics},
    VOLUME = {24},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {373--389},
}

@article {PSS09,
    AUTHOR = {Pelsmajer, Michael J. and Schaefer, Marcus and
              {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Removing even crossings on surfaces},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {30},
      YEAR = {2009},
    NUMBER = {7},
     PAGES = {1704--1717},
      ISSN = {0195-6698},
}

@article {PSS07d,
    AUTHOR = {Pelsmajer, Michael J. and Schaefer, Marcus and
              {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Removing Even Crossings},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {97},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {489--500},
      ISSN = {0095-8956},
     CODEN = {JCBTB8},
}


@incollection {PSS07b,
    AUTHOR = {Pelsmajer, Michael J. and Schaefer, Marcus and
              {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Crossing number of graphs with rotation systems},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4875},
     PAGES = {3--12},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2008},
}

@incollection {AFP16,
    AUTHOR = {Alam, Md. Jawaherul and Fink, Martin and Pupyrev, Sergey},
     TITLE = {The bundled crossing number},
 BOOKTITLE = {Graph drawing and network visualization},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9801},
     PAGES = {399--412},
 PUBLISHER = {Springer, Cham},
      YEAR = {2016},
   MRCLASS = {68R10 (05C62)},
  MRNUMBER = {3627102},
}

@incollection {FHSV16,
    AUTHOR = {Fink, Martin and Hershberger, John and Suri, Subhash and
              Verbeek, Kevin},
     TITLE = {Bundled crossings in embedded graphs},
 BOOKTITLE = {L{ATIN} 2016: theoretical informatics},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9644},
     PAGES = {454--468},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2016},
   MRCLASS = {68R10 (68W25)},
  MRNUMBER = {3492547},
       DOI = {10.1007/978-3-662-49529-2_34},
       URL = {http://dx.doi.org/10.1007/978-3-662-49529-2_34},
}

%use AADM18
@ARTICLE{AADM16,
   author = {{Alfaro}, Carlos~A. and {Arroyo}, Alan and {Derun{\'a}r}, Marek and {Mohar}, Bojan
	},
    title = "{The crossing number of the cone of a graph}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1608.07680},
      note = {\arxiv{1608.07680} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics},
     year = 2016,
    month = aug,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160807680A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {AADM18,
    AUTHOR = {Alfaro, Carlos A. and Arroyo, Alan and Der\v{n}\'{a}r, Marek and
              Mohar, Bojan},
     TITLE = {The crossing number of the cone of a graph},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {32},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {2080--2093},
      ISSN = {0895-4801},
   MRCLASS = {68R10 (05C62)},
  MRNUMBER = {3841614},
MRREVIEWER = {W. G. Brown},
       DOI = {10.1137/17M1115320},
       URL = {https://doi.org/10.1137/17M1115320},
}

@article{PSS09d,
   author = {Pelsmajer, Michael J. and Schaefer, Marcus and \v{S}tefankovi\v{c}, Daniel},
   title = {Crossing Numbers of Graphs with Rotation Systems},
   journal = {Algorithmica},
   publisher = {Springer New York},
   issn = {0178-4617},
   keyword = {Computer Science},
   pages = {679-702},
   volume = {60},
   issue = {3},
   url = {http://dx.doi.org/10.1007/s00453-009-9343-y},
   note = {10.1007/s00453-009-9343-y},
   year = {2011}
}

@article {dFR85,
    AUTHOR = {de Fraysseix, Hubert and Rosenstiehl, Pierre},
     TITLE = {A characterization of planar graphs by {T}r\'emaux orders},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal of the J\'anos Bolyai
              Mathematical Society},
    VOLUME = {5},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {127--135},
      ISSN = {0209-9683},
}


@article {R99,
    AUTHOR = {Rosenstiehl, Pierre},
     TITLE = {A new proof of the {G}auss interlace conjecture},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {23},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {3--13},
      ISSN = {0196-8858},
}

%don't use PSS08c, use PSS10
@misc{PSS08c,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Removing Independently Even Crossings. A Note on the Independent Odd Crossing Number",
  note = "Unpublished Manuscript.",
}

@article{PSS10,
author = {Michael J. Pelsmajer and Marcus Schaefer and Daniel \v{S}tefankovi\v{c}},
title = {Removing Independently Even Crossings},
publisher = {SIAM},
year = {2010},
journal = {SIAM Journal on Discrete Mathematics},
volume = {24},
number = {2},
pages = {379-393},
keywords = {crossing number; independent odd crossing number; HananiTutte theorem},
url = {http://link.aip.org/link/?SJD/24/379/1},
doi = {10.1137/090765729}
}

%same as PSS07d, don't use, use PSS07d
@Article{PSS06,
    AUTHOR = {Pelsmajer, Michael J. and Schaefer, Marcus and
              {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Removing even crossings},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {97},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {489--500},
}

@techreport{PSS05,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Odd crossing number is not crossing number",
  institution = "DePaul University",
  year = "2005",
  number = "TR05-005",
  month="April",
}


@techreport{HN09,
  title={ Two-page Book Embedding and Clustered Graph Planarity},
  author={Hong, Seok-Hee and Nagamochi, Hiroshi},
  year = "2009",
  number = "Technical Report 2009-004",
  school = "Kyoto University",
}

@techreport{PSS08b,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Despina Stasi",
  title =        "Strong {H}anani-{T}utte on the Projective Plane",
  institution = "DePaul University",
  year = "2008",
  number = "TR08-003",
  month="April",
}

@unpublished{PSS09b,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Despina Stasi",
  title =        "Strong {H}anani-{T}utte on the Projective Plane",
  note = "To appear in {\em SIAM J. Discrete Mathematics}.",
}

@InProceedings{PSS05b,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =       "Odd Crossing Number Is Not Crossing Number",
  booktitle =   "Graph Drawing",
  series =  "Lecture Notes in Computer Science",
  pages =   "386--396",
  year =    "2005",
  volume =  "3843",
  editor =  "Patrick Healy and Nikola S. Nikolov",
  publisher =   "Springer",
  ISBN =    "3-540-31425-3",
}

@article {HK04,
    AUTHOR = {Healy, Patrick and Kuusik, Ago},
     TITLE = {Algorithms for multi-level graph planarity testing and layout},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {320},
      YEAR = {2004},
    NUMBER = {2-3},
     PAGES = {331--344},
      ISSN = {0304-3975},
}

@incollection {HH08,
    AUTHOR = {Harrigan, Martin and Healy, Patrick},
     TITLE = {Practical level planarity testing and layout with embedding constraints},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4875},
     PAGES = {62--68},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2008},
}

@InProceedings{MTW09,
  title =	"Hardness of embedding simplicial complexes in {$\RN^d$}",
  author =	"Ji\v{r}\'{\i} Matou{\v{s}}ek and Martin Tancer and Uli Wagner",
  booktitle =	"Proceedings of the Twentieth Annual {ACM}-{SIAM}
		 Symposium on Discrete Algorithms, {SODA} 2009, New
		 York, {NY}, {USA}, January 4-6, 2009",
  publisher =	"SIAM",
  year = 	"2009",
  editor =	"Claire Mathieu",
  pages =	"855--864",
}

@incollection{dF08,
    AUTHOR = {de Fraysseix, Hubert},
     TITLE = {Tr\'emaux trees and planarity},
 BOOKTITLE = {The {I}nternational {C}onference on {T}opological and {G}eometric {G}raph {T}heory},
    SERIES = {Electron. Notes Discrete Math.},
    VOLUME = {31},
     PAGES = {169--180},
 PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
      YEAR = {2008},
}



@article{PSS08,
 author = {Michael J. Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}},
 title = {Odd Crossing Number and Crossing Number Are Not the Same},
 JOURNAL = {Discrete Comput. Geom.},
 FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
 volume = {39},
 number = {1},
 year = {2008},
 issn = {0179-5376},
 pages = {442--454},
 doi = {http://dx.doi.org/10.1007/s00454-008-9058-x},
 publisher = {Springer-Verlag New York, Inc.},
 address = {Secaucus, NJ, USA},
 }

@book {GPP09,
     TITLE = {Twentieth anniversary volume. {D}iscrete \& {C}omputational
              {G}eometry},
    EDITOR = {Goodman, Jacob E. and Pach, J{\'a}nos and Pollack, Richard},
      NOTE = {Reprinted from Discrete Comput. Geom. {{\bf{3}}9} (2008), no.
              1-3},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2009},
     PAGES = {xviii+635},
      ISBN = {978-0-387-87362-6},
   MRCLASS = {01A75 (51-06 52-06 65D18 68U05)},
  MRNUMBER = {MR2516504 (2009m:01016)},
}


@techreport{PSS05c,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Crossing Numbers and Parameterized Complexity",
  institution = "DePaul University",
  year = "2006",
  number = "TR06-013",
  month="August",
}

@inproceedings{PSS07c,
  author    = {Michael J. Pelsmajer and
               Marcus Schaefer and
               {\v S}tefankovi{\v c}},
  title     = {Crossing Numbers and Parameterized Complexity},
  booktitle = {Graph Drawing},
  publisher =	"Springer",
  year      = {2007},
   volume =	"4875",
  pages     = {31-36},
 series =	"Lecture Notes in Computer Science",
 editor =	"Seok-Hee Hong and Takao Nishizeki and Wu Quan",
}




@techreport{PSS05d,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Crossing Number of Graphs with Rotation Systems",
  institution = "DePaul University",
  year = "2005",
  number = "TR05-017",
  month="November",
}

@techreport{PSS06b,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Removing Even Crossings, Continued",
  institution = "DePaul University",
  year = "2006",
  number = "TR06-016",
  month="August",
}

%don't use, use PSS08
@Article{PSS06c,
  author =       "Michael J.~Pelsmajer and Marcus Schaefer and Daniel {\v S}tefankovi{\v c}",
  title =        "Odd crossing number and crossing number are not the same",
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},

  year = "2006",
  note = "To appear."
}

@Article{C34,
  author =       "Chojnacki (Haim Hanani), Chaim",
  title =        "{\"{U}}ber wesentlich unpl{\"{a}}ttbare {K}urven im drei-dimensionalen {R}aume",
  journal =      "Fundamenta Mathematicae",
  volume =       "23",
  pages =        "135--142",
  year =         "1934",
}


%use FP11
@article{FP10,
      author       = "Fulek, Radoslav and Pach, J{\'a}nos",
      title        = "A computational approach to Conway's thrackle conjecture",
      journal = {CoRR},
      volume = {abs/1002.3904},
      ee={http://arxiv.org/abs/1002.3904},
      month        = "Feb",
      year         = "2010",
  note =  	"\arxiv{1002.3904} (last accessed 9/21/2017)",
}

@article {FP11,
    AUTHOR = {Fulek, Radoslav and Pach, J\'{a}nos},
     TITLE = {A computational approach to {C}onway's thrackle conjecture},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {44},
      YEAR = {2011},
    NUMBER = {6-7},
     PAGES = {345--355},
      ISSN = {0925-7721},
   MRCLASS = {05C62},
  MRNUMBER = {2785903},
       DOI = {10.1016/j.comgeo.2011.02.001},
       URL = {https://doi.org/10.1016/j.comgeo.2011.02.001},
}


@inproceedings {L72,
    AUTHOR = {Levow, Roy B.},
     TITLE = {On {T}utte's algebraic approach to the theory of crossing
              numbers},
 BOOKTITLE = {Proceedings of the {T}hird {S}outheastern {C}onference on
              {C}ombinatorics, {G}raph {T}heory, and {C}omputing},
     PAGES = {315--314},
 PUBLISHER = {Florida Atlantic Univ.},
   ADDRESS = {Boca Raton, Fla.},
      YEAR = {1972},
}


@article {S91,
    AUTHOR = {Sarkaria, K. S.},
     TITLE = {A one-dimensional {W}hitney trick and {K}uratowski's graph
              planarity criterion},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {73},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {79--89},
      ISSN = {0021-2172},
       DOI = {10.1007/BF02773426},
       URL = {http://dx.doi.org/10.1007/BF02773426},
}

@incollection {S91b,
    AUTHOR = {Shor, Peter W.},
     TITLE = {Stretchability of pseudolines is {NP}-hard},
 BOOKTITLE = {Applied geometry and discrete mathematics},
    SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.},
    VOLUME = {4},
     PAGES = {531--554},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1991},
}

@article{LM09,
  author = {Martin Loebl and Gregor Masbaum},
  title = {On the optimality of the Arf invariant formula for graph polynomials},
  journal = {CoRR},
  volume = {abs/0908.2925},
  ee        = {http://arxiv.org/abs/0908.2925},
  year = {2009},
  note = {\arxiv{0908.2925} (last accessed 9/21/2017)},
}

@article {LM11,
    AUTHOR = {Loebl, Martin and Masbaum, Gregor},
     TITLE = {On the optimality of the {A}rf invariant formula for graph
              polynomials},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {226},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {332--349},
      ISSN = {0001-8708},
}

@article {AR88,
    AUTHOR = {Archdeacon, Dan and Richter, R. Bruce},
     TITLE = {On the parity of crossing numbers},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {12},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {307--310},
      ISSN = {0364-9024},
}



@InProceedings{CGP98,
  author =       "Zhi-Zhong Chen and Michelangelo Grigni and Christos
                 Papadimitriou",
  title =        "Planar map graphs",
  pages =        "514--523",
  ISBN =         "0-89791-962-9",
  booktitle =    "Proceedings of the 30th Annual {ACM} Symposium on
                 Theory of Computing ({STOC}-98)",
  publisher =    "ACM Press",
  address =      "New York",
  year =         "1998",
}

@Article{E91,
  author =       "Max J. Egenhofer",
  title =        "Reasoning About Binary Topological Relations",
  journal =      "Lecture Notes in Computer Science",
  volume =       "525",
  pages =        "143--160",
  year =         "1991",
  coden =        "LNCSD9",
  ISSN =         "0302-9743"
}

@incollection {E72,
     TITLE = {Unsolved problems},
 BOOKTITLE = {Combinatorics (Proc. Conf. Combinatorial Math., Math. Inst.,
              Oxford, 1972)},
     PAGES = {351--363},
      NOTE = {Chairman: P. Erd\H{o}s},
 PUBLISHER = {Inst. Math. Appl.},
   ADDRESS = {Southend},
      YEAR = {1972},
   MRCLASS = {05-XX},
  MRNUMBER = {MR0363917 (51 \#172)},
MRREVIEWER = {B. Manvel},
}


@article{K30,
  author = "H. Kneser",
  title = "{G}eschlossene {F}l{\"{a}}chen in dreidimensionalen {M}annigfaltigkeiten",
  journal = "Jahresbericht der Deutschen Mathematikver-Vereinigung",
  vol = "38",
  pages = "248--260",
  year = "1930"
}

@Article{H61,
  author = "Wolfgang Haken",
  title = "Theorie der {N}ormalfl{\"a}chen",
  journal = "Acta Mathematica",
  volume = "105",
  pages ="245--375",
  year = "1961"
}

%use AP13 instead
@unpublished{AP12?,
  author = "Ackerman, Eyal and Pinchasi, Rom",
  title = "On the Degenerate Crossing Number",
  note = "Unpublished manuscript",
  year = "2012",
  url = {http://http://www2.math.technion.ac.il/~room/ps_files/dcross.pdf},
}

@article{AP13,
    AUTHOR = {Ackerman, Eyal and Pinchasi, Rom},
     TITLE = {On the degenerate crossing number},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {49},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {695--702},
      ISSN = {0179-5376},
}

@Article{HLP99,
  author = "Joel Hass and Jeffrey Lagarias and Nicholas Pippenger",
  title = "The computational complexity of knot and link
  problems.",
  journal = "Journal of ACM",
  volume = "46",
  year = "1999",
  number= "2",
  pages = "185--211"
}

@InProceedings{AHT02,
  author = "Ian Agol and Joel Hass and William Thurston",
  title = "3-manifold knot genus is {NP}-complete",
  booktitle =    "Proceedings of the 33th Annual {ACM} Symposium on
                 Theory of Computing ({STOC}-2002)",
  year =         "2002",
}

@article {H76,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Parity of numbers of crossings for complete {$n$}-partite
              graphs},
   JOURNAL = {Math. Slovaca},
  FJOURNAL = {Matematicky \v Casopis Slovenskej Akad\'emie Vied},
    VOLUME = {26},
      YEAR = {1976},
    NUMBER = {2},
     PAGES = {77--95},
}

@misc{H76a,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Aufgabe 750},
   JOURNAL = {Elem. Math.},
  FJOURNAL = {Elemente der Mathematik},
    VOLUME = {31},
      YEAR = {1976},
    NUMBER = {5},
     PAGES = {121},
}

@incollection {H78,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Crossings on edges in drawings of complete multipartite
              graphs},
 BOOKTITLE = {Combinatorics ({P}roc. {F}ifth {H}ungarian {C}olloq.,
              {K}eszthely, 1976), {V}ol. {I}},
    SERIES = {Colloq. Math. Soc. J\'anos Bolyai},
    VOLUME = {18},
     PAGES = {539--551},
 PUBLISHER = {North-Holland, Amsterdam-New York},
      YEAR = {1978},
}

@incollection {H85,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Drawings of graphs and multiple crossings},
 BOOKTITLE = {Graph theory with applications to algorithms and computer
              science ({K}alamazoo, {M}ich., 1984)},
    SERIES = {Wiley-Intersci. Publ.},
     PAGES = {413--421},
 PUBLISHER = {Wiley, New York},
      YEAR = {1985},
}

@inproceedings {H88,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Drawings of the cycle graph},
 booktitle = {Nineteenth Southeastern Conference on Combinatorics, Graph
              Theory, and Computing (Baton Rouge, LA, 1988)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {66},
      YEAR = {1988},
     PAGES = {15--22},
      ISSN = {0384-9864},
}

@incollection{H88b,
  title={{D}arstellungen des vollst{\"a}ndigen {G}raphen ohne {K}anten mit wenigen {K}reuzungen},
  author={Harborth, Heiko},
  booktitle = {Graphen und Netzwerke—Theorie und Anwendungen},
  journal={33. Intern. Wiss. Koll. TH Ilmenau 1988, Heft 4, C2},
  publisher = {TH Ilmenau},
  pages={179-181},
  year={1988}
}

@article {K76,
    AUTHOR = {Kleitman, Daniel J.},
     TITLE = {A note on the parity of the number of crossings of a graph},
   JOURNAL = {J. Combinatorial Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {21},
      YEAR = {1976},
    NUMBER = {1},
     PAGES = {88--89},
}

@incollection {APS08,
    AUTHOR = {Agarwal, Pankaj K. and Pach, J{\'a}nos and Sharir, Micha},
     TITLE = {State of the union (of geometric objects)},
 BOOKTITLE = {Surveys on discrete and computational geometry},
    SERIES = {Contemp. Math.},
    VOLUME = {453},
     PAGES = {9--48},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2008},
}

@article {PS99,
    AUTHOR = {Pach, J\'{a}nos and Sharir, Micha},
     TITLE = {On the boundary of the union of planar convex sets},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {21},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {321--328},
}


@article {SS04,
    AUTHOR = {Smorodinsky, Shakhar and Sharir, Micha},
     TITLE = {Selecting points that are heavily covered by pseudo-circles,
              spheres or rectangles},
   JOURNAL = {Combin. Probab. Comput.},
  FJOURNAL = {Combinatorics, Probability and Computing},
    VOLUME = {13},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {389--411},
      ISSN = {0963-5483},
}

@article {ANPPSS04,
    AUTHOR = {Agarwal, Pankaj K. and Nevo, Eran and Pach, J{\'a}nos and
              Pinchasi, Rom and Sharir, Micha and Smorodinsky, Shakhar},
     TITLE = {Lenses in arrangements of pseudo-circles and their
              applications},
   JOURNAL = {J. ACM},
  FJOURNAL = {Journal of the ACM},
    VOLUME = {51},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {139--186},
      ISSN = {0004-5411},
}


@article {LPS97,
    AUTHOR = {Lov{\'a}sz, Laszlo and Pach, J\'{a}nos and Szegedy, Mario},
     TITLE = {On {C}onway's thrackle conjecture},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {18},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {369--376},
      ISSN = {0179-5376},
}

@Article{ELT94,
  title =	"An Algorithm for Drawing a Hierarchical Graph",
  author =	"Peter Eades and Xuemin Lin and Roberto Tamassia",
  journal =	"Int. J. Comput. Geometry Appl",
  year = 	"1996",
  number =	"2",
  volume =	"6",
  bibdate =	"2003-12-03",
  pages =	"145--156",
}

@article{LE03,
 author = {Lin, Xuemin and Eades, Peter},
 title = {Towards area requirements for drawing hierarchically planar graphs},
 journal = {Theor. Comput. Sci.},
 volume = {292},
 number = {3},
 year = {2003},
 issn = {0304-3975},
 pages = {679--695},
 publisher = {Elsevier Science Publishers Ltd.},
 address = {Essex, UK},
 }


@Article{EFLN06,
  author =	"Peter Eades and Qingwen Feng and Xuemin Lin and
		 Hiroshi Nagamochi",
  title =	"Straight-Line Drawing Algorithms for Hierarchical
		 Graphs and Clustered Graphs",
  journal =	"Algorithmica",
  volume =	"44",
  number =	"1",
  pages =	"1--32",
  month =	jan,
  year = 	"2006",
  ISSN = 	"0178-4617 (print), 1432-0541 (electronic)",
}

@incollection{HP96,
  author =	"Lenwood S. Heath and Sriram V. Pemmaraju",
  title =	"Recognizing leveled-planar dags in linear time",
  booktitle =	"Graph Drawing, GD'95",
  pages =	"300--311",
  year = 	"1996",
  volume =	"1027",
    SERIES = {Lecture Notes in Comput. Sci.},
  editor =	"Franz J. Brandenburg",
  publisher =	"Springer-Verlag",
  address =	"Berlin",
}

@article {HP99,
    AUTHOR = {Heath, Lenwood S. and Pemmaraju, Sriram V.},
     TITLE = {Stack and queue layouts of directed acyclic graphs. {II}},
   JOURNAL = {SIAM J. Comput.},
  FJOURNAL = {SIAM Journal on Computing},
    VOLUME = {28},
      YEAR = {1999},
    NUMBER = {5},
     PAGES = {1588--1626},
      ISSN = {0097-5397},
}


@article {PT04,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Monotone drawings of planar graphs},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {46},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {39--47},
      ISSN = {0364-9024},
}

@InProceedings{PT112,
  title =	"Monotone Crossing Number",
  author =	"J{\'a}nos Pach and G{\'e}za T{\'o}th",
  publisher =	"Springer",
  year = 	"2011",
  volume =	"7034",
  booktitle =	"Graph Drawing",
  editor =	"Marc J. van Kreveld and Bettina Speckmann",
  ISBN = 	"978-3-642-25877-0",
  pages =	"278--289",
  series =	"Lecture Notes in Computer Science",
}

@ARTICLE{PT11,
     AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
    title = "{Monotone drawings of planar graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1101.0967},
      note = {\arxiv{1101.0967} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 68R10, 05C62},
     year = 2011,
    month = jan,
}


@inproceedings{EFL96,
 author = {Eades, Peter and Feng, Qing-Wen and Lin, Xuemin},
 title = {Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1190},
 PUBLISHER = {Springer},
 year = {1997},
 pages = {113--128},
 address = {London, UK},
 }

 @inproceedings{PRTT04,
 author = {Pach, J\'{a}nos and Radoici\'{c}, Rado\v{s} and Tardos, G\'{a}bor and T\'{o}th, G\'{e}za},
 title = {Improving the crossing lemma by finding more crossings in sparse graphs: [extended abstract]},
 booktitle = {SCG '04: Proceedings of the twentieth annual symposium on Computational geometry},
 year = {2004},
 isbn = {1-58113-885-7},
 pages = {68--75},
 location = {Brooklyn, New York, USA},
 doi = {http://doi.acm.org/10.1145/997817.997831},
 publisher = {ACM},
 address = {New York, NY, USA},
 }


@unpublished{ES07,
author = "Esther Ezra and Micha Sharir",
title = "Lower Envelopes of $3$-Intersecting Surfaces in {$\RN^3$}",
note = "Unpublished manuscript",
year = "2007",
}

@incollection {PS04,
    AUTHOR = {Pach, J{\'a}nos and Sharir, Micha},
     TITLE = {Geometric incidences},
 BOOKTITLE = {Towards a theory of geometric graphs},
    SERIES = {Contemp. Math.},
    VOLUME = {342},
     PAGES = {185--223},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
}


@book {MT01,
    AUTHOR = {Mohar, Bojan and Thomassen, Carsten},
     TITLE = {Graphs on surfaces},
    SERIES = {Johns Hopkins Studies in the Mathematical Sciences},
 PUBLISHER = {Johns Hopkins University Press},
   ADDRESS = {Baltimore, MD},
      YEAR = {2001},
}


@unpublished{N05,
    AUTHOR = {Norine, Serguei},
     TITLE = {{P}faffian Graphs, T-joins, and Crossing Numbers},
     note = "{T}o be published by Combinatorica",
}

@article {N08,
    AUTHOR = {Norine, Serguei},
     TITLE = {Pfaffian graphs, {$T$}-joins and crossing numbers},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
              the Theory of Computing},
    VOLUME = {28},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {89--98},
}

@incollection {P04,
    AUTHOR = {Pach, J{\'a}nos},
     TITLE = {Geometric Graph Theory},
 BOOKTITLE = {Handbook of discrete and computational geometry, 2nd edition},
    SERIES = {CRC Press Ser. Discrete Math. Appl.},
     PAGES = {219--238},
 PUBLISHER = {CRC},
   ADDRESS = {Boca Raton, FL},
      YEAR = {2004},
}

@article{vK33,
    author = "E. R. van Kampen",
    title = {Komplexe in euklidischen {R}\"{a}umen},
    volume = "9",
    pages = "72--78",
    year = "1933",
    publisher = "Springer",
    number = "1",
    month = "December",
    journal = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t Hamburg},
}

@article {W85,
    AUTHOR = {Wu, Wen Jun},
     TITLE = {On the planar imbedding of linear graphs. {I}},
   JOURNAL = {J. Systems Sci. Math. Sci.},
  FJOURNAL = {Journal of Systems Science and Mathematical Sciences. Xitong
              Kexue yu Shuxue},
    VOLUME = {5},
      YEAR = {1985},
    NUMBER = {4},
     PAGES = {290--302},
      ISSN = {1000-0577},
}

@article {ABSS97,
    AUTHOR = {Arora, Sanjeev and Babai, L{\'a}szl{\'o} and Stern, Jacques
              and Sweedyk, Z.},
     TITLE = {The hardness of approximate optima in lattices, codes, and
              systems of linear equations},
      NOTE = {34th Annual Symposium on Foundations of Computer Science (Palo
              Alto, CA, 1993)},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {54},
      YEAR = {1997},
    NUMBER = {2, part 2},
     PAGES = {317--331},
      ISSN = {0022-0000},
}

@phdthesis{L98,
 author = "Sebastian Leipert",
 title = "Level Planarity Testing and Embedding in Linear Time",
 year = "1998",
 school = "Universit{\"{a}}t zu K{\"{o}}ln",
 address = "K{\"{o}}ln",
 }

@article {JL02,
    AUTHOR = {J{\"u}nger, Michael and Leipert, Sebastian},
     TITLE = {Level planar embedding in linear time},
      NOTE = {Graph drawing and representations (Prague, 1999)},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {6},
      YEAR = {2002},
     PAGES = {no. 1, 67--113},
      ISSN = {1526-1719},
}


@incollection {JLM98,
    AUTHOR = {J{\"u}nger, Michael and Leipert, Sebastian and Mutzel, Petra},
     TITLE = {Level planarity testing in linear time},
 BOOKTITLE = {Graph drawing ({M}ontr\'eal, {QC}, 1998)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1547},
     PAGES = {224--237},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1998},
}

@InCollection{JLM98a,
  author =	"Michael J{\"u}nger and Sebastian Leipert and Petra
		 Mutzel",
  title =	"Pitfalls of using ${PQ}$-trees in automatic graph
		 drawing",
  booktitle =	"Proceedings of the 5th International Symposium on
		 Graph Drawing, GD'97 (Rome, Italy, September 18-20,
		 1997)",
  pages =	"193--204",
  year = 	"1998",
  volume =	"1353",
  series =	"LNCS",
  editor =	"Giuseppe DiBattista",
  publisher =	"Springer-Verlag",
  address =	"Berlin",
}

@InProceedings{EBFK09,
  title =	"On the Characterization of Level Planar Trees by Minimal Patterns",
  author =	"Alejandro Estrella-Balderrama and J. Joseph Fowler and Stephen G. Kobourov",
  publisher =	"Springer",
  year = 	"2009",
  volume =	"5849",
  booktitle =	"Graph Drawing",
  editor =	"David Eppstein and Emden R. Gansner",
  ISBN = 	"978-3-642-11804-3",
  pages =	"69--80",
  series =	"Lecture Notes in Computer Science",
}

@article {HKL04,
    AUTHOR = {Healy, Patrick and Kuusik, Ago and Leipert, Sebastian},
     TITLE = {A characterization of level planar graphs},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {280},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {51--63},
      ISSN = {0012-365X},
}



@Article{BSBHKMSC01,
  title =	"A Satisfiability Formulation of Problems on Level
		 Graphs",
  author =	"Bert Randerath and Ewald Speckenmeyer and Endre Boros
		 and Peter L. Hammer and Alexander Kogan and Kazuhisa
		 Makino and Bruno Simeone and Ondrej Cepek",
  journal =	"Electronic Notes in Discrete Mathematics",
  year = 	"2001",
  volume =	"9",
  pages =	"269--277",
}



@misc{H11,
 author = "Patrick Healy",
 howpublished  = "Personal communication",
 month = "January",
 year = "2011",
}

@article {W86,
    AUTHOR = {Wu, Wen Jun},
     TITLE = {On the planar imbedding of linear graphs (continued)},
   JOURNAL = {J. Systems Sci. Math. Sci.},
  FJOURNAL = {Journal of Systems Science and Mathematical Sciences. Xitong
              Kexue yu Shuxue},
    VOLUME = {6},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {23--35},
      ISSN = {1000-0577},
}

%use T12 instead
@incollection{T11?,
     AUTHOR = {T{\'o}th, G{\'e}za},
     TITLE = {A better bound for pair-crossing number},
    booktitle = {Thirty Essays on Geometric Graph Theory},
    publisher = {Springer},
    editor = {Pach, J\'{a}nos},
    pages = {xx+430},
    isbn = {978-1-4614-0109-4},
    year = 2012,
}

@incollection{T12,
     AUTHOR = {T{\'o}th, G{\'e}za},
     TITLE = {A better bound for the pair-crossing number},
    booktitle = {Thirty Essays on Geometric Graph Theory},
    publisher = {Springer},
    editor = {Pach, J\'{a}nos},
    pages = {563--567},
    isbn = {978-1-4614-0109-4},
    year = 2012,
}

@incollection{CG07,
    AUTHOR = {Chimani, Markus and Gutwenger, Carsten},
     TITLE = {Algorithms for the hypergraph and the minor crossing number
              problems},
 BOOKTITLE = {Algorithms and computation},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4835},
     PAGES = {184--195},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2007},
}

@article {PT00,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Which crossing number is it anyway?},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {80},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {225--246},
      ISSN = {0095-8956},
}

@incollection {PT06,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Degenerate crossing numbers},
 BOOKTITLE = {Computational geometry (SCG'06)},
     PAGES = {255--258},
 PUBLISHER = {ACM},
   ADDRESS = {New York},
      YEAR = {2006},
}

@article {PT09,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Degenerate crossing numbers},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {41},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {376--384},
      ISSN = {0179-5376},
}


@article {PT00b,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Thirteen problems on crossing numbers},
   JOURNAL = {Geombinatorics},
  FJOURNAL = {Geombinatorics},
    VOLUME = {9},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {194--207},
      ISSN = {1065-7371},
}

@article {S08,
    AUTHOR = {Sz{\'e}kely, L{\'a}szl{\'o} A.},
     TITLE = {An optimality criterion for the crossing number},
   JOURNAL = {Ars Math. Contemp.},
  FJOURNAL = {Ars Mathematica Contemporanea},
    VOLUME = {1},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {32--37},
      ISSN = {1855-3966},
}

@article {S66,
    AUTHOR = {Shapiro, Arnold},
     TITLE = {Obstructions to the imbedding of a complex in a euclidean
              space. {I}. {T}he first obstruction},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {66},
      YEAR = {1957},
     PAGES = {256--269},
      ISSN = {0003-486X},
   MRCLASS = {55.0X},
  MRNUMBER = {MR0089410 (19,671a)},
MRREVIEWER = {S. T. Hu},
}

@article{W44,
     title = {The Self-Intersections of a Smooth n-Manifold in 2n-Space},
     author = {Whitney, Hassler},
     journal = {The Annals of Mathematics},
     volume = {45},
     number = {2},
     series = {Second Series},
     pages = {220--246},
     url = {http://www.jstor.org/stable/1969265},
     ISSN = {0003486X},
     abstract = {},
     language = {},
     year = {1944},
     publisher = {Annals of Mathematics},
    }


@unpublished{S10,
    author = "Schaefer, Marcus",
    title = "Removing Incident Crossings",
    note = "Unpublished Manuscript",
    year = "2010"
}


%use S14
@inproceedings{S1?,
    author = "Schaefer, Marcus",
    editor = "B{\'a}r{\'a}ny, I. and B{\"o}r{\"o}czky, K. J.  and T\'{o}th, G. Fejes  and  Pach, J.",
    title = "Hanani-{T}utte and Related Results",
    booktitle = "Geometry---Intuitive, Discrete, and Convex---A Tribute to L{\'a}szl{\'o} Fejes T{\'o}th",
    series = "Bolyai Society Mathematical Studies",
    publisher = "Springer",
    address = "Berlin",
    note = "To appear.",
}

@incollection{S14,
    author = "Schaefer, Marcus",
    editor = "B{\'a}r{\'a}ny, I. and B{\"o}r{\"o}czky, K. J.  and T\'{o}th, G. Fejes  and  Pach, J.",
    title = "Hanani-{T}utte and Related Results",
    booktitle = "Geometry---Intuitive, Discrete, and Convex---A Tribute to L{\'a}szl{\'o} Fejes T{\'o}th",
    series = "Bolyai Society Mathematical Studies",
    volume = {24},
    publisher = "Springer",
    address = "Berlin",
    year = "2014",
    isbn = {978-3-642-41497-8},
}

@incollection{S10b,
    author = "Schaefer, Marcus",
    title = "Complexity of Some Geometric and Topological Problems",
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {5849},
     PAGES = {334-344},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2010},
}

@InProceedings{T07,
  title =	"Note on the Pair-Crossing Number and the Odd-Crossing Number",
  author =	"G{\'e}za T{\'o}th",
   booktitle =	"Proceedings of the 19th Annual Canadian Conference on
		 Computational Geometry, {CCCG} 2007, August 20-22,
		 2007, Carleton University, Ottawa, Canada",
  publisher =	"Carleton University, Ottawa, Canada",
  year = 	"2007",
  editor =	"Prosenjit Bose",
  ISBN = 	"978-0-7709-0520-0",
  pages =	"3--6",
}

@article {T08,
    AUTHOR = {T{\'o}th, G{\'e}za},
    TITLE = {Note on the Pair-crossing Number and the Odd-crossing Number},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {39},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {791--799},
}

@incollection {P00,
    AUTHOR = {Pach, J{\'a}nos},
     TITLE = {Crossing numbers},
 BOOKTITLE = {Discrete and computational geometry (Tokyo, 1998)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1763},
     PAGES = {267--273},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
}

@article {H31,
    AUTHOR = {Hopf, Heinz},
     TITLE = {\"{U}ber die {A}bbildungen der dreidimensionalen {S}ph\"are
              auf die {K}ugelfl\"ache},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {104},
      YEAR = {1931},
    NUMBER = {1},
     PAGES = {637--665},
      ISSN = {0025-5831},
}

@InProceedings{R99,
  author = "Wojciech Rytter",
  title = "Algorithms on compressed strings and arrays",
  booktitle = "Proceedings of 26th Annual Conference on Current Trends in Theory and Practice of Infomatics.",
  year = "1999"
}

@article {S04,
    AUTHOR = {Sz{\'e}kely, L{\'a}szl{\'o} A.},
     TITLE = {A successful concept for measuring non-planarity of graphs:
              the crossing number},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {276},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {331--352},
}

@InProceedings{S05,
  title =	"Progress on Crossing Number Problems",
  author =	"L{\'a}szl{\'o} A. Sz{\'e}kely",
  booktitle =	"{SOFSEM} 2005: Theory and Practice of Computer
		 Science, 31st Conference on Current Trends in Theory
		 and Practice of Computer Science, Liptovsk{\'y}
		 {J}{\'a}n, Slovakia, January 22-28, 2005, Proceedings",
  publisher =	"Springer",
  year = 	"2005",
  volume =	"3381",
  editor =	"Peter Vojt{\'a}s and M{\'a}ria Bielikov{\'a} and
		 Bernadette Charron-Bost and Ondrej S{\'y}kora",
  ISBN = 	"3-540-24302-X",
  pages =	"53--61",
  series =	"Lecture Notes in Computer Science",
}

@article {T70,
    AUTHOR = {Tutte, William T.},
     TITLE = {Toward a theory of crossing numbers},
   JOURNAL = {J. Combinatorial Theory},
    VOLUME = {8},
      YEAR = {1970},
     PAGES = {45--53},
}

@book {TV06,
    AUTHOR = {Tao, Terence and Vu, Van},
     TITLE = {Additive combinatorics},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {105},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2006},
}

@article{ZL77,
    author = "Jacob Ziv and Abraham Lempel",
    title = "A Universal Algorithm for Sequential Data Compression",
    journal = "IEEE Transactions on Information Theory",
    volume = "23",
    number = "3",
    pages = "337-343",
    year = "1977"
}

@incollection{V04,
    author = "Pavel Valtr",
    title = "On the Pair-Crossing Number",
    booktitle = "Combinatorial and Computational Geometry",
    SERIES = {Math. Sci. Res. Inst. Publ.},
   VOLUME = {52},
     PAGES = {569--575},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2005},
}

@incollection {MR2178340,
    AUTHOR = {Valtr, Pavel},
     TITLE = {On the pair-crossing number},
 BOOKTITLE = {Combinatorial and computational geometry},
    SERIES = {Math. Sci. Res. Inst. Publ.},
    VOLUME = {52},
     PAGES = {569--575},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2005},
   MRCLASS = {05C10 (05C62)},
  MRNUMBER = {MR2178340},
}



@InProceedings{DEG99,
  author =       "Tamal Dey and Herbert Edelsbrunner and Sumanta Guha",
  title = "Computational Topology",
  editor = "B. Chazelle and J.E. Goodman and R. Pollack",
  booktitle = "Advances in Discrete and Computational Geometry",
  volume = "223 of Contemporary Mathematics",
  publisher = "American Mathematical Society",
  year = "1999"
}



@Article{DG99,
  author =       "Tamal Dey and Sumanta Guha",
  title =        "Transforming Curves on Surfaces",
  journal =      "JCSS: Journal of Computer and System Sciences",
  volume =       "58",
  number = "2",
  pages = "297-325",
  year =         "1999",
}


@misc{BE99,
  title = {{Emerging challenges in computational topology}},
  author = {Marshall Wayne Bern and David Eppstein and others},
  eprint = {cs.CG/9909001},
  howpublished = {ACM Computing Research Repository},
  month = {September},
  year = {1999}}

@unpublished{V?,
    author = "Pavel Valtr",
    title = "On the Pair-Crossing Number",
    note = "Manuscript",
}

@article {BD93,
    AUTHOR = {Bienstock, Daniel and Dean, Nathaniel},
     TITLE = {Bounds for rectilinear crossing numbers},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {17},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {333--348},
}

@article {dBN88,
    AUTHOR = {Di Battista, Giuseppe and Nardelli, Enrico},
     TITLE = {Hierarchies and planarity theory},
   JOURNAL = {IEEE Trans. Systems Man Cybernet.},
  FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Systems, Man, and Cybernetics},
    VOLUME = {18},
      YEAR = {1988},
    NUMBER = {6},
     PAGES = {1035--1046 (1989)},
      ISSN = {0018-9472},
}


%don't use
@misc{vdH05,
  author = "Holst, Hein van der",
  title = "Some recent results in topological graph theory (Invited Talk)",
  howpublished = "Eurocomb 2005",
  note="{\ttfamily http://www.math.tu-berlin.de/\linebreak[0]EuroComb05/\linebreak[0]%
  Talks/\linebreak[0]Invited/\linebreak[0]VIII-vanderHolst\linebreak[0].pdf}
(accessed August 3rd, 2006)",
  }

  @article {vdHP09,
    AUTHOR = {van der Holst, Hein and Pendavingh, Rudi},
     TITLE = {On a graph property generalizing planarity and flatness},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
              the Theory of Computing},
    VOLUME = {29},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {337--361},
      ISSN = {0209-9683},
       DOI = {10.1007/s00493-009-2219-6},
       URL = {http://dx.doi.org/10.1007/s00493-009-2219-6},
}


  @article {vdH09,
    AUTHOR = {van der Holst, Hein},
     TITLE = {A polynomial-time algorithm to find a linkless embedding of a
              graph},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {99},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {512--530},
      ISSN = {0095-8956},
       DOI = {10.1016/j.jctb.2008.10.002},
       URL = {http://dx.doi.org/10.1016/j.jctb.2008.10.002},
}


@article {vdH07,
    AUTHOR = {van der Holst, Hein},
     TITLE = {Algebraic characterizations of outerplanar and planar graphs},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {28},
      YEAR = {2007},
    NUMBER = {8},
     PAGES = {2156--2166},
}

%Historical Papers

@article {W70,
    AUTHOR = {Watkins, Mark E.},
     TITLE = {A special crossing number for bipartite graphs: {A} research
              problem. },
   JOURNAL = {Ann. New York Acad. Sci.},
    VOLUME = {175},
      YEAR = {1970},
     PAGES = {405--410},
}

@book {T06,
    AUTHOR = {Tucker, Alan},
     TITLE = {Applied combinatorics},
   EDITION = {Fifth},
 PUBLISHER = {John Wiley \& Sons Inc.},
   ADDRESS = {New York},
      YEAR = {2006},
     PAGES = {496},
}

@incollection {ACNS82,
    AUTHOR = {Ajtai, M. and Chv{\'a}tal, V. and Newborn, M. M. and
              Szemer{\'e}di, E.},
     TITLE = {Crossing-free subgraphs},
 BOOKTITLE = {Theory and practice of combinatorics},
    SERIES = {North-Holland Math. Stud.},
    VOLUME = {60},
     PAGES = {9--12},
 PUBLISHER = {North-Holland},
   ADDRESS = {Amsterdam},
      YEAR = {1982},
}

@Book{L83,
  author =	"F. T. Leighton",
  title =	"Complexity Issues in {VLSI}: Optimal Layouts for the
		 Shuffle-Exchange Graph and Other Networks",
  year = 	"1983",
  publisher =	"MIT Press",
  address =	"Cambridge, MA",
}

@article {L84,
    AUTHOR = {Leighton, Frank Thomson},
     TITLE = {New lower bound techniques for {VLSI}},
   JOURNAL = {Math. Systems Theory},
  FJOURNAL = {Mathematical Systems Theory. An International Journal on
              Mathematical Computing Theory},
    VOLUME = {17},
      YEAR = {1984},
    NUMBER = {1},
     PAGES = {47--70},
}

@article {CELR97,
    AUTHOR = {Cohen, R. F. and Eades, P. and Lin, Tao and Ruskey, F.},
     TITLE = {Three-dimensional graph drawing},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {17},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {199--208},
      ISSN = {0178-4617},
}

@inproceedings{S90a,
 author = {Schnyder, Walter},
 title = {Embedding planar graphs on the grid},
 booktitle = {Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms},
 series = {SODA '90},
 year = {1990},
 isbn = {0-89871-251-3},
 location = {San Francisco, California, USA},
 pages = {138--148},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA},
}

%use DMS14
@ARTICLE{DMS13,
   author = {{Dujmovi\,{c}}, Vida and {Morin}, Pat and {Sheffer}, Adam},
    title = "{Crossings in Grid Drawings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1301.0303},
      note = {\arxiv{1301.0303} (last accessed 9/21/2017)},
     year = 2013,
    month = jan,
}


@article {DMS14,
    author = {{Dujmovi\,{c}}, Vida and {Morin}, Pat and {Sheffer}, Adam},
     TITLE = {Crossings in Grid Drawings},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {21},
      YEAR = {2014},
      pages = {P1.41},
    NUMBER = {1},
      ISSN = {1077-8926},
}

@misc{S09,
 author = {Chaitanya Swamy},
 title = {{CO}452/652: Integer Programming},
 year = {2009},
 note = {Homework Assignment at \url{http://www.math.uwaterloo.ca/~cswamy/courses/co652/as3.pdf} (last accessed 1/9/2013)},
}

@article {OZ09,
    AUTHOR = {Oporowski, Bogdan and Zhao, David},
     TITLE = {Coloring graphs with crossings},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {309},
      YEAR = {2009},
    NUMBER = {9},
     PAGES = {2948--2951},
}

@misc {O13,
    AUTHOR = {Oporowski, Bogdan},
    howpublished = {Personal communication},
    month = "March",
    year = "2013",
}


@article {N03,
    AUTHOR = {Nahas, Nagi H.},
     TITLE = {On the crossing number of {$K_{m,n}$}},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {10},
      YEAR = {2003},
     PAGES = {Note 8},
}


@InProceedings{MK09,
  title =	"Minimal Obstructions for 1-Immersions and Hardness of
		 1-Planarity Testing",
  author =	"Vladimir P. Korzhik and Bojan Mohar",
  publisher =	"Springer",
  year = 	"2008",
  volume =	"5417",
  booktitle =	"Graph Drawing",
  crossref =	"conf/gd/2008",
  editor =	"Ioannis G. Tollis and Maurizio Patrignani",
  ISBN = 	"978-3-642-00218-2",
  pages =	"302--312",
  series =	"Lecture Notes in Computer Science",
}

@article {H06,
    AUTHOR = {Hlin{\v{e}}n{\'y}, Petr},
     TITLE = {Crossing number is hard for cubic graphs},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {96},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {455--471},
      ISSN = {0095-8956},
}

@incollection {G72,
    AUTHOR = {Guy, Richard K.},
     TITLE = {Crossing numbers of graphs},
 BOOKTITLE = {Graph theory and applications ({P}roc. {C}onf., {W}estern
              {M}ichigan {U}niv., {K}alamazoo, {M}ich., 1972; dedicated to
              the memory of {J}. {W}. {T}. {Y}oungs)},
     PAGES = {111--124},
 PUBLISHER = {Lecture Notes in Math., Vol. 303, Springer, Berlin},
      YEAR = {1972},
}

@article {B91,
    AUTHOR = {Bienstock, Daniel},
     TITLE = {Some provably hard crossing number problems},
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      YEAR = {1991},
    NUMBER = {5},
     PAGES = {443--459},
      ISSN = {0179-5376},
}

@article {CK97,
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      YEAR = {1997},
    NUMBER = {3},
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      ISSN = {0218-1959},
}

@article {K68,
    AUTHOR = {Kainen, Paul C.},
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   JOURNAL = {J. Combinatorial Theory},
    VOLUME = {5},
      YEAR = {1968},
     PAGES = {374--377},
}

@incollection {K74,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {Some recent results in topological graph theory},
 BOOKTITLE = {Graphs and combinatorics ({P}roc. {C}apital {C}onf., {G}eorge
              {W}ashington {U}niv., {W}ashington, {D}.{C}., 1973)},
     PAGES = {76--108. Lecture Notes in Math., Vol. 406},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1974},
}

@article {KW78,
    AUTHOR = {Kainen, Paul C. and White, Arthur T.},
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   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {2},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {181--187},
      ISSN = {0364-9024},
}

@article {K72b,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {On the stable crossing number of cubes},
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  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {36},
      YEAR = {1972},
     PAGES = {55--62},
      ISSN = {0002-9939},
}

@article {M65,
    AUTHOR = {Moon, J. W.},
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   JOURNAL = {J. Soc. Indust. Appl. Math.},
    VOLUME = {13},
      YEAR = {1965},
     PAGES = {506--510},
}

@article {EG73,
    AUTHOR = {Erd{\H{o}}s, P. and Guy, R. K.},
     TITLE = {Crossing number problems},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {80},
      YEAR = {1973},
     PAGES = {52--58},
      ISSN = {0002-9890},
}

@incollection {ZB07,
   author = {Zheng, Lanbo and Buchheim, Christoph},
   title = {A New Exact Algorithm for the Two-Sided Crossing Minimization Problem},
   booktitle = {Combinatorial Optimization and Applications},
   series = {Lecture Notes in Computer Science},
   editor = {Dress, Andreas and Xu, Yinfeng and Zhu, Binhai},
   publisher = {Springer Berlin / Heidelberg},
   pages = {301-310},
   volume = {4616},
   year = {2007}
}

@article {HS71,
    AUTHOR = {Harary, Frank and Schwenk, Allen},
     TITLE = {Trees with {H}amiltonian square},
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  FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
    VOLUME = {18},
      YEAR = {1971},
     PAGES = {138--140},
      ISSN = {0025-5793},
}

@article {HS72,
    AUTHOR = {Harary, Frank and Schwenk, Allen},
     TITLE = {A new crossing number for bipartite graphs},
   JOURNAL = {Utilitas Math.},
  FJOURNAL = {Utilitas Mathematica. An International Journal of Discrete and
              Combinatorial Mathematics, and Statistical Design},
    VOLUME = {1},
      YEAR = {1972},
     PAGES = {203--209},
      ISSN = {0315-3681},
}

@article {H69,
    AUTHOR = {Harary, Frank},
     TITLE = {Determinants, permanents and bipartite graphs},
   JOURNAL = {Math. Mag.},
  FJOURNAL = {Delta. University of Wisconsin},
    VOLUME = {42},
      YEAR = {1969},
     PAGES = {146--148},
      ISSN = {0011-801x},
}

@article{G60,
  author = {Richard K. Guy},
  title = {A combinatorial problem},
  journal = {Nabla (Bull. Malayan Math. Soc)},
  pages = {68--72},
  volume = {7},
  year = {1960},
}

@article {BW10,
    AUTHOR = {Beineke, Lowell and Wilson, Robin},
     TITLE = {The early history of the brick factory problem},
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    VOLUME = {32},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {41--48},
      ISSN = {0343-6993},
}


@InCollection{S16,
author="Sz{\'e}kely, L{\'a}szl{\'o} A.",
editor="Gera, Ralucca and Hedetniemi, Stephen and Larson, Craig",
title="Tur{\'a}n's {B}rick {F}actory Problem: The Status of the Conjectures of {Z}arankiewicz and {H}ill",
bookTitle="Graph Theory: Favorite Conjectures and Open Problems  - 1",
year="2016",
publisher="Springer",
pages="211--230",
abstract="In this chapter, we explore the history and the status of the Zarankiewicz crossing number conjecture and the Hill crossing number conjecture, on drawing complete bipartite and complete graphs in the plane with a minimum number of edge crossings. We discuss analogous problems on other surfaces and in different models of drawing.",
isbn="978-3-319-31940-7",
doi="10.1007/978-3-319-31940-7_13",
url="https://doi.org/10.1007/978-3-319-31940-7_13"
}

@article{K79,
     title = {The Utilities Problem},
     author = {Kullman, David E.},
     journal = {Mathematics Magazine},
     volume = {52},
     number = {5},
     pages = {299-302},
     url = {http://www.jstor.org/stable/2689782},
     ISSN = {0025570X},
     language = {English},
     year = {1979},
     publisher = {Mathematical Association of America},
    }

@Misc{Vx,
  author =	"V{\v{r}}{\v{t}}o, Imrich",
  title =	"Crossing Numbers of Graphs: a Bibliography",
  year = 	"2011",
  note = "Last updated: January 15th, 2014",
  howpublished = "Available at \url{ftp://ftp.ifi.savba.sk/pub/imrich/crobib.pdf} (last accessed 2/3/2020)",

}

@inbook{BCGJM?,
 author ={Christoph Buchheim and Markus Chimani and Carsten Gutwenger and Michael Juenger and Petra Mutzel},
 title = {Crossings and Planarization},
 chapter = {2},
 pages = {43--86},
 crossref = {T13?},
}

@inbook{BKR?,
 author ={Bl\"{a}sius, Thomas and Kobourov, Stephen G. and Rutter, Ignaz},
 title = {Simultaneous Embeddings of Planar Graphs},
  chapter = {11},
 pages = {349--382},
 crossref = {T13?},
}


@inbook{KT?,
 author ={Kakoulis, Konstantinos G. and Tollis, Ioannis G.},
 title = {Labeling algorithms},
  chapter = {15},
 pages = {489--516},
 crossref = {T13?},
}

@book{T13?,
    editor = {Roberto Tamassia},
    title = {Handbook of Graph Drawing and Visualization},
    series = {Discrete Mathematics and Its Applications},
    publisher = {Chapman and Hall/CRC},
    isbn = {1584884126},
    year = {2013},
}

@article {H64,
    AUTHOR = {Harary, Frank},
     TITLE = {Recent results in topological graph theory},
   JOURNAL = {Acta Math. Acad. Sci. Hungar},
  FJOURNAL = {Acta Mathematica Academiae Scientiarum Hungaricae},
    VOLUME = {15},
      YEAR = {1964},
     PAGES = {405--411},
      ISSN = {0001-5954},
}

@article {HH63,
    AUTHOR = {Harary, Frank and Hill, Anthony},
     TITLE = {On the number of crossings in a complete graph},
   JOURNAL = {Proc. Edinburgh Math. Soc. (2)},
  FJOURNAL = {Proceedings of the Edinburgh Mathematical Society. Series II},
    VOLUME = {13},
      YEAR = {1962/1963},
     PAGES = {333--338},
      ISSN = {0013-0915},
}

@article {H65,
    AUTHOR = {Harary, Frank},
     TITLE = {On minimally nonplanar graphs},
   JOURNAL = {Ann. Univ. Sci. Budapest. E\"otv\"os Sect. Math.},
  FJOURNAL = {Annales Universitatis Scientiarum Budapestinensis de Rolando
              E\"otv\"os Nominatae. Sectio Mathematica},
    VOLUME = {8},
      YEAR = {1965},
     PAGES = {13--15},
      ISSN = {0524-9007},
}

@Article{BG07,
  title =	"Algorithms for Graphs Embeddable with Few Crossings
		 per Edge",
  author =	"Alexander Grigoriev and Hans L. Bodlaender",
  journal =	"Algorithmica",
  year = 	"2007",
  number =	"1",
  volume =	"49",
  pages =	"1--11",
}

@article {GJ69,
    AUTHOR = {Guy, Richard K. and Jenkyns, T. A.},
     TITLE = {The toroidal crossing number of {$K_{m,n}$}},
   JOURNAL = {J. Combinatorial Theory},
    VOLUME = {6},
      YEAR = {1969},
     PAGES = {235--250},
}

@article {GJS68,
    AUTHOR = {Guy, Richard K. and Jenkyns, Tom and Schaer, Jonathan},
     TITLE = {The toroidal crossing number of the complete graph},
   JOURNAL = {J. Combinatorial Theory},
    VOLUME = {4},
      YEAR = {1968},
     PAGES = {376--390},
}


@article {M09,
    AUTHOR = {Mohar, Bojan},
     TITLE = {The genus crossing number},
   JOURNAL = {Ars Math. Contemp.},
  FJOURNAL = {Ars Mathematica Contemporanea},
    VOLUME = {2},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {157--162},
      ISSN = {1855-3966},
}

@incollection {BEJKMW06,
    AUTHOR = {Buchheim, Christoph and Ebner, Dietmar and J{\"u}nger, Michael
              and Klau, Gunnar W. and Mutzel, Petra and Weiskircher,
              Ren{\'e}},
     TITLE = {Exact crossing minimization},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {3843},
     PAGES = {37--48},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

@article {PT97,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Graphs drawn with few crossings per edge},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
              the Theory of Computing},
    VOLUME = {17},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {427--439},
      ISSN = {0209-9683},
}

@article {V08,
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    VOLUME = {396},
      YEAR = {2008},
    NUMBER = {1-3},
     PAGES = {294--300},
      ISSN = {0304-3975},
}

%use KPRSV11
@article{KPRSV08,
  title =	"Obfuscated Drawings of Planar Graphs",
  author =	"Mihyun Kang and Oleg Pikhurko and Alexander Ravsky and
		 Mathias Schacht and Oleg Verbitsky",
  journal =	"CoRR",
  year = 	"2008",
  volume =	"abs/0803.0858",
  note =  	"\arxiv{0803.0858}, see version 3 (last accessed 9/21/2017)",
}

@article{KPRSV11,
  author    = {Mihyun Kang and
               Oleg Pikhurko and
               Alexander Ravsky and
               Mathias Schacht and
               Oleg Verbitsky},
  title     = {Untangling planar graphs from a specified vertex position - Hard cases},
  journal   = {Discrete Applied Mathematics},
  volume    = {159},
  number    = {8},
  pages     = {789--799},
  year      = {2011},
  url       = {https://doi.org/10.1016/j.dam.2011.01.011},
  doi       = {10.1016/j.dam.2011.01.011},
  timestamp = {Mon, 05 Jun 2017 20:49:02 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/dam/KangPRSV11},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@article {K70,
    AUTHOR = {Kleitman, Daniel J.},
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}

@article {BD92,
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      ISSN = {0364-9024},
}

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    NUMBER = {6},
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      ISSN = {0364-9024},
}

@book {G72b,
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 PUBLISHER = {American Mathematical Society Providence, R.I.},
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@book {C1889,
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     part = {2},
 PUBLISHER = {Adam and Charles Black},
   ADDRESS = {Edinburgh},
      YEAR = {1889},
     PAGES = {xxiv+616},
}

@misc{S04x,
   author = "David Singmaster",
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@article {S69,
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@article {S23,
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              {P}olygonen von gerader {S}eitenzahl},
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@article {AFH09,
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@inproceedings {AFHK09,
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 BOOKTITLE = {Proceedings of the {F}ortieth {S}outheastern {I}nternational
              {C}onference on {C}ombinatorics, {G}raph {T}heory and
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}
		
@article {PRS94,
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      YEAR = {1994},
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@inproceedings {GR92,
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 BOOKTITLE = {Proceedings of the {T}wenty-third {S}outheastern
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   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {90},
      YEAR = {1992},
     PAGES = {193--203},
      ISSN = {0384-9864},
}

@article {RSP91,
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      YEAR = {1991},
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}

@incollection {PRS91,
    AUTHOR = {Piazza, B. L. and Ringeisen, R. D. and Stueckle, S. K.},
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@article {R96,
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@article {RB78,
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@article {BR80,
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@incollection {A09,
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@incollection {SSSV95,
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              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Book embeddings and crossing numbers},
 BOOKTITLE = {Graph-theoretic concepts in computer science ({H}errsching,
              1994)},
    SERIES = {Lecture Notes in Comput. Sci.},
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 PUBLISHER = {Springer},
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      YEAR = {1995},
}

@article {SSSV07,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, Ondrej and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {On {$k$}-planar crossing numbers},
   JOURNAL = {Discrete Appl. Math.},
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@article {SSSV96,
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      YEAR = {1996},
    NUMBER = {4},
     PAGES = {413--424},
      ISSN = {0364-9024},
}

@MastersThesis{W05,
    author     =     {Winterbach, Wynand},
    title     =     {{The crossing number of a graph in the plane}},
    school     =     {University of Stellenbosch},
    address     =     {South Africa},
    year     =     {2005},
    }

@article {N68,
    AUTHOR = {Nicholson, T. A. J.},
     TITLE = {Permutation procedure for minimising the number of crossings
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   JOURNAL = {Proc. Inst. Elec. Engrs.},
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@incollection{CLTR85,
    AUTHOR = {Chung, Fan R. K. and Leighton, Frank Thomson and Rosenberg,
              Arnold L.},
     TITLE = {Embedding graphs in books: a layout problem with applications
              to {VLSI} design},
 BOOKTITLE = {Graph theory with applications to algorithms and computer
              science ({K}alamazoo, {M}ich., 1984)},
    SERIES = {Wiley-Intersci. Publ.},
     PAGES = {175--188},
 PUBLISHER = {Wiley},
   ADDRESS = {New York},
      YEAR = {1985},
}

@article{BK79,
    AUTHOR = {Bernhart, Frank and Kainen, Paul C.},
     TITLE = {The book thickness of a graph},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {27},
      YEAR = {1979},
    NUMBER = {3},
     PAGES = {320--331},
      ISSN = {0095-8956},
}

@inproceedings{BS84,
 author = {Buss, Jonathan F. and Shor, Peter W.},
 title = {On the pagenumber of planar graphs},
 booktitle = {Proceedings of the sixteenth annual ACM symposium on Theory of computing},
 series = {STOC '84},
 year = {1984},
 isbn = {0-89791-133-4},
 pages = {98--100},
 publisher = {ACM},
 address = {New York, NY, USA},
}

@inproceedings{K90,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {The book thickness of a graph. {II}},
 BOOKTITLE = {Proceedings of the {T}wentieth {S}outheastern {C}onference on
              {C}ombinatorics, {G}raph {T}heory, and {C}omputing ({B}oca
              {R}aton, {FL}, 1989)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {71},
      YEAR = {1990},
     PAGES = {127--132},
      ISSN = {0384-9864},
}

@article {MNKF90,
    AUTHOR = {Masuda, Sumio and Nakajima, Kazuo and Kashiwabara, Toshinobu
              and Fujisawa, Toshio},
     TITLE = {Crossing minimization in linear embeddings of graphs},
   JOURNAL = {IEEE Trans. Comput.},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Computers},
    VOLUME = {39},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {124--127},
      ISSN = {0018-9340},
}

@incollection{BB05,
year={2005},
isbn={978-3-540-24132-4},
booktitle={Graph-Theoretic Concepts in Computer Science},
volume={3353},
series={Lecture Notes in Computer Science},
editor={Hromkovic, Juraj and Nagl, Manfred and Westfechtel, Bernhard},
title={Crossing Reduction in Circular Layouts},
publisher={Springer Berlin Heidelberg},
author={Baur, Michael and Brandes, Ulrik},
pages={332-343}
}

@inproceedings{MKNF87,
    AUTHOR = {Masuda, Sumio and Kashiwabara, Toshinobu and Nakajima, Kazuo
              and Fujisawa, Toshio},
     TITLE = {On the {NP}-Completeness of a Computer Network Layout Problem},
   booktitle = {International Symposium on Circuits and Systems},
      YEAR = {1987},
     PAGES = {292-295},
     publisher = {IEEE},
      lccn = {86083020},
}

@article {GJMP80,
    AUTHOR = {Garey, M. R. and Johnson, D. S. and Miller, G. L. and
              Papadimitriou, C. H.},
     TITLE = {The complexity of coloring circular arcs and chords},
   JOURNAL = {SIAM J. Algebraic Discrete Methods},
  FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on
              Algebraic and Discrete Methods},
    VOLUME = {1},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {216--227},
      ISSN = {0196-5212},
}

@InProceedings{U88,
    AUTHOR = {Unger, Walter},
     TITLE = {On the {$k$}-colouring of circle-graphs},
 BOOKTITLE = {S{TACS} 88 ({B}ordeaux, 1988)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {294},
     PAGES = {61--72},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1988},
}

@InProceedings{U92,
  title =	"The Complexity of Colouring Circle Graphs (Extended
		 Abstract)",
  author =	"Walter Unger",
  booktitle =	"9th Annual Symposium on Theoretical Aspects of
		 Computer Science",
  address =	"Cachan, France",
  month =	"13--15~" # feb,
  year = 	"1992",
  series =	"lncs",
  volume =	"577",
  publisher =	"Springer",
  pages =	"389--400",
}

@article {CM07,
    AUTHOR = {Cimikowski, Robert J. and Mumey, Brendan},
     TITLE = {Approximating the fixed linear crossing number},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {155},
      YEAR = {2007},
    NUMBER = {17},
     PAGES = {2202--2210},
      ISSN = {0166-218X},
}

@article{C06,
author={Cimikowski, Robert J.},
title={An analysis of some linear graph layout heuristics},
year={2006},
issn={1381-1231},
journal={Journal of Heuristics},
volume={12},
issue={3},
publisher={Kluwer Academic Publishers},
pages={143-153},
}

@inproceedings {C92,
    AUTHOR = {Cimikowski, Robert J.},
     TITLE = {Graph planarization and skewness},
 BOOKTITLE = {Proceedings of the {T}wenty-third {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory, and {C}omputing ({B}oca {R}aton, {FL}, 1992)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {88},
      YEAR = {1992},
     PAGES = {21--32},
      ISSN = {0384-9864},
}

@article {GS04,
author = {Glebsky, Lev Yu. and Salazar, Gelasio},
title = {The crossing number of {$C_m \times C_n$} is as conjectured for $n \geq m(m+1)$},
journal = {Journal of Graph Theory},
volume = {47},
number = {1},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1097-0118},
pages = {53--72},
year = {2004},
}

@article {K72,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {A lower bound for crossing numbers of graphs with applications
              to {$K_{n}$}, {$K_{p,\,q}$}, and {$Q(d)$}},
   JOURNAL = {J. Combinatorial Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {12},
      YEAR = {1972},
     PAGES = {287--298},
}

@article {M99,
    AUTHOR = {Mohar, Bojan},
     TITLE = {A linear time algorithm for embedding graphs in an arbitrary
              surface},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {12},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {6--26},
      ISSN = {0895-4801},
}

@incollection {SSSV03,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, Ondrej and Sz{\'e}kely,
              Laszlo A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Bounds for convex crossing numbers},
 BOOKTITLE = {Computing and combinatorics},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2697},
     PAGES = {487--495},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
}

@incollection {SSSV04,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, Ondrej and Sz{\'e}kely,
              Laszlo A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {The gap between crossing numbers and convex crossing numbers},
 BOOKTITLE = {Towards a theory of geometric graphs},
    SERIES = {Contemp. Math.},
    VOLUME = {342},
     PAGES = {249--258},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
}

@InProceedings{ST99,
  title =	"Circular Drawings of Biconnected Graphs",
  author =	"Janet M. Six and Ioannis G. Tollis",
  booktitle =	"Algorithm Engineering and Experimentation, International Workshop {ALENEX} '99, Baltimore, {MD},
		 {USA}, January 15-16, 1999, Selected Papers",
  publisher =	"Springer",
  year = 	"1999",
  volume =	"1619",
  editor =	"Michael T. Goodrich and Catherine C. McGeoch",
  ISBN = 	"3-540-66227-8",
  pages =	"57--73",
  series =	"Lecture Notes in Computer Science",
}

@article {R03,
    AUTHOR = {Riskin, Adrian},
     TITLE = {On the outerplanar crossing numbers of {$K_{m,n}$}},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {39},
      YEAR = {2003},
     PAGES = {16--20},
      ISSN = {1183-1278},
}

@article {FPSS12b,
    AUTHOR = {Fulek, Radoslav and Pelsmajer, Michael J. and Schaefer, Marcus
              and {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Adjacent crossings do matter},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {16},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {759--782},
      ISSN = {1526-1719},
}

@InProceedings{FPSS11,
    AUTHOR = {Fulek, Radoslav and Pelsmajer, Michael and Schaefer, Marcus and \v{S}tefankovi\v{c}, Daniel},
     TITLE = {Adjacent Crossings Do Matter},
 publisher =	"Springer",
  year = 	"2011",
  volume =	"7034",
  booktitle =	"Graph Drawing",
  editor =	"Marc J. van Kreveld and Bettina Speckmann",
  ISBN = 	"978-3-642-25877-0",
  pages =	"343--354",
  series =	"Lecture Notes in Computer Science",
}

%use FPS11 instead
@misc{FPSS1x,
   AUTHOR = {Fulek, Radoslav and Pelsmajer, Michael and Schaefer, Marcus and \v{S}tefankovi\v{c}, Daniel},
     TITLE = {Adjacent Crossings Do Matter},
     note = {Manuscript},
}

@InProceedings{FPSS11b,
   AUTHOR = {Fulek, Radoslav and Pelsmajer, Michael and Schaefer, Marcus and \v{S}tefankovi\v{c}, Daniel},
      title = {Hanani-{T}utte and Monotone Drawings},
   booktitle = {Graph-Theoretic Concepts in Computer Science},
   series = {Lecture Notes in Computer Science},
   editor = {Kolman, Petr and Kratochv{\i}l, Jan},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-25869-5},
   keyword = {Computer Science},
   pages = {283-294},
   volume = {6986},
   year = {2011}
}

@incollection{FPSS12,
   AUTHOR = {Fulek, Radoslav and Pelsmajer, Michael and Schaefer, Marcus and \v{S}tefankovi\v{c}, Daniel},
     title = {Hanani-{T}utte, Monotone Drawings, and Level-Planarity},
    booktitle = {Thirty Essays on Geometric Graph Theory},
    publisher = {Springer},
    editor = {Pach, J\'{a}nos},
    pages = {263-287},
    isbn = {978-1-4614-0109-4},
    year = 2012,
}

%use FK19
@ARTICLE{FK17,
   author = {Fulek, Radoslav and {Kyn{\v c}l}, Jan},
    title = "{Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1709.00508},
      note = {\arxiv{1709.00508} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Discrete Mathematics, 05C10, 57M15},
     year = 2017,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170900508F},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {FK19,
    AUTHOR = {Fulek, Radoslav and Kyn\v{c}l, Jan},
     TITLE = {Counterexample to an {E}xtension of the {H}anani-{T}utte
              {T}heorem on the {S}urface of {G}enus 4},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
              the Theory of Computing},
    VOLUME = {39},
      YEAR = {2019},
    NUMBER = {6},
     PAGES = {1267--1279},
      ISSN = {0209-9683},
   MRCLASS = {05C10 (57M15)},
  MRNUMBER = {4055204},
       DOI = {10.1007/s00493-019-3905-7},
       URL = {https://doi.org/10.1007/s00493-019-3905-7},
}

@article{W17,
  author    = {Jiun{-}Jie Wang},
  title     = {Layouts for Plane Graphs on Constant Number of Tracks},
  journal   = {CoRR},
  volume    = {abs/1708.02114},
  year      = {2017},
  url       = {http://arxiv.org/abs/1708.02114},
  note = {\arxiv{1708.02114} (last accessed 9/21/2017)},
  timestamp = {Tue, 05 Sep 2017 10:03:46 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/corr/abs-1708-02114},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

%use HT18
@misc{HT17u,
    author = {Hlin{\v{e}}ny, Petr and Thomassen, Carsten},
    title = {Deciding Parity of Graph Crossing Number},
    howpublished = {\url{http://www.fi.muni.cz/~hlineny/papers/paritycross-SIAM.pdf} (last accessed 9/14/2017)},
    year = {2017},
}

@article {HT18,
    AUTHOR = {Hlin\v{e}n\'{y}, Petr and Thomassen, Carsten},
     TITLE = {Deciding parity of graph crossing number},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {32},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {1962--1965},
      ISSN = {0895-4801},
   MRCLASS = {05C62 (68Q25 68R10)},
  MRNUMBER = {3836175},
       DOI = {10.1137/17M1137231},
       URL = {https://doi.org/10.1137/17M1137231},
}
	


@article {BFM06,
    AUTHOR = {Bokal, Drago and Fijav{\v{z}}, Ga{\v{s}}per and Mohar, Bojan},
     TITLE = {The minor crossing number},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {20},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {344--356},
      ISSN = {0895-4801},
}


@article {BFW08,
    AUTHOR = {Bokal, Drago and Fijav{\v{z}}, Ga{\v{s}}per and Wood, David
              R.},
     TITLE = {The minor crossing number of graphs with an excluded minor},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {15},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {Research Paper 4},
      ISSN = {1077-8926},
}

@incollection {BJMP06,
    AUTHOR = {Buchheim, Christoph and J{\"u}nger, Michael and Menze, Annette
              and Percan, Merijam},
     TITLE = {Bimodal crossing minimization},
 BOOKTITLE = {Computing and combinatorics},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4112},
     PAGES = {497--506},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

@incollection {BZ06,
    AUTHOR = {Buchheim, Christoph and Zheng, Lanbo},
     TITLE = {Fixed linear crossing minimization by reduction to the maximum
              cut problem},
 BOOKTITLE = {Computing and combinatorics},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4112},
     PAGES = {507--516},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

@PhDthesis{C08b,
  title =	"Computing crossing numbers",
  author =	"Markus Chimani",
  year = 	"2008",
  school = {Technische Universit{\"{a}}t Dortmund},
  address = {Dortmund},
}

@article {DP98,
    AUTHOR = {Dey, T. K. and Pach, J.},
     TITLE = {Extremal problems for geometric hypergraphs},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {19},
      YEAR = {1998},
    NUMBER = {4},
     PAGES = {473--484},
      ISSN = {0179-5376},
}


@article {BCSV10,
    AUTHOR = {Bokal, Drago and Czabarka, {\'E}va and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {General lower bounds for the minor crossing number of graphs},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {44},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {463--483},
      ISSN = {0179-5376},
}

@article {RT95,
    AUTHOR = {Richter, R. Bruce  and Thomassen, Carsten},
     TITLE = {Intersections of curve systems and the crossing number of
              {$C_5\times C_5$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {13},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {149--159},
      ISSN = {0179-5376},
}

@InProceedings{W06,
  title =	"On a Geometric Generalization of the Upper Bound
		 Theorem",
  author =	"Uli Wagner",
  publisher =	"IEEE Computer Society",
  year = 	"2006",
  booktitle =	"FOCS: IEEE Symposium on Foundations of Computer Science (FOCS)",
  ISBN = 	"0-7695-2720-5",
  pages =	"635--645",
}

@incollection{SSSV97,
    AUTHOR = {Shahrokhi, Farhad and S\'ykora, Ondrej and Sz\'ekely, L\'aszl\'o A.
              and Vr\v{t}o, Imrich},
     TITLE = {Crossing numbers: bounds and applications},
 BOOKTITLE = {Intuitive geometry ({B}udapest, 1995)},
    SERIES = {Bolyai Soc. Math. Stud.},
    VOLUME = {6},
     PAGES = {179--206},
 PUBLISHER = {J\'anos Bolyai Math. Soc.},
   ADDRESS = {Budapest},
      YEAR = {1997},
}

@incollection {SSSV93,
    AUTHOR = {Shahrokhi, Farhad and Sz{\'e}kely, L{\'a}szl{\'o} A. and
              S{\'y}kora, Ondrej and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Improved bounds for the crossing numbers on surfaces of genus
              {$g$}},
 BOOKTITLE = {Graph-theoretic concepts in computer science ({U}trecht,
              1993)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {790},
     PAGES = {388--395},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1994},
}



@article {SSSV96a,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, O. and Sz{\'e}kely, L{\'a}szl{\'o} A. and
              Vr{\v{t}}o, Imrich},
     TITLE = {The crossing number of a graph on a compact {$2$}-manifold},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {123},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {105--119},
      ISSN = {0001-8708},
}

@article {SSSV96b,
    AUTHOR = {Shahrokhi, Farhad and Sz{\'e}kely, L{\'a}szl{\'o} A. and S{\'y}kora, O. and
              Vr{\v{t}}o, Imrich},
     TITLE = {Drawings of graphs on surfaces with few crossings},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {16},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {118--131},
      ISSN = {0178-4617},
}


@article {ACF09,
    AUTHOR = {Albertson, Michael O. and Cranston, Daniel W. and Fox, Jacob},
     TITLE = {Crossings, colorings, and cliques},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {Research Paper 45},
      ISSN = {1077-8926},
}

@inproceedings {FG09,
    AUTHOR = {Feder, Elie and Garber, David},
     TITLE = {The orchard crossing number of an abstract graph},
 BOOKTITLE = {Proceedings of the {F}ortieth {S}outheastern {I}nternational
              {C}onference on {C}ombinatorics, {G}raph {T}heory and
              {C}omputing},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {197},
      YEAR = {2009},
     PAGES = {3--19},
      ISSN = {0384-9864},
}

@article {K73,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {Thickness and coarseness of graphs},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"at
              Hamburg},
    VOLUME = {39},
      YEAR = {1973},
     PAGES = {88--95},
      ISSN = {0025-5858},
}

@book{MS01,
  title={1000 {P}lay {T}hinks: {P}uzzles, {P}aradoxes, {I}llusions \& {G}ames},
  author={Moscovich, I. and Stewart, I.},
  isbn={9780761118268},
  year={2001},
  pages = {420},
  publisher={Workman Pub.}
}

@ARTICLE{O71,
author={ Owens, Alvin},
journal={Transactions on Circuit Theory},
title={On the biplanar crossing number},
year={1971},
month={March},
volume={18},
number={2},
publisher = {IEEE},
pages={ 277 - 280},
ISSN={0018-9324},}

@article {M83,
    AUTHOR = {Mansfield, Anthony},
     TITLE = {Determining the thickness of graphs is {NP}-hard},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {93},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {9--23},
      ISSN = {0305-0041},
}

@incollection {CSSV06,
    AUTHOR = {Czabarka, {\'E}va and S{\'y}kora, Ondrej and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Biplanar crossing numbers. {I}. {A} survey of results and
              problems},
 BOOKTITLE = {More sets, graphs and numbers},
    SERIES = {Bolyai Soc. Math. Stud.},
    VOLUME = {15},
     PAGES = {57--77},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

@article {CSSV08,
    AUTHOR = {Czabarka, {\'E}va and S{\'y}kora, Ondrej and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Biplanar crossing numbers. {II}. {C}omparing crossing numbers
              and biplanar crossing numbers using the probabilistic method},
   JOURNAL = {Random Structures Algorithms},
  FJOURNAL = {Random Structures \& Algorithms},
    VOLUME = {33},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {480--496},
      ISSN = {1042-9832},
}

@Article{EHLP11,
  title =	"5-Coloring Graphs with 4 Crossings",
  author =	"Rok Erman and Fr{\'e}d{\'e}ric Havet and Bernard
		 Lidick{\'y} and Ondrej Pangr{\'a}c",
  journal =	"SIAM J. Discrete Math",
  year = 	"2011",
  number =	"1",
  volume =	"25",
  pages =	"401--422",
}

@ARTICLE{CH11,
   author =	"Victor Campos and Fr{\'e}d{\'e}ric Havet",
    title = "{$5$-choosability of graphs with $2$ crossings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
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}

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@article {JS03,
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}

%use TT16
@ARTICLE{TT10,
   author = "Hiroyuki Tanaka and Masakazu Teragaito",
    title = "{Triple crossing numbers of graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
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 primaryClass = "math.CO",
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     year = 2010,
    month = feb,
}

@article {TT16,
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  MRNUMBER = {3467806},
MRREVIEWER = {J. Lauri},
}

@article {EW94,
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}

@inproceedings{EMKW86,
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  year={1986}
}

@InProceedings{CJS08,
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@incollection {GJPSS06,
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@article {L00,
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      ISSN = {0179-5376},
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@article {CGMW10,
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@article {GT01b,
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@article {N01,
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@article {N98,
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@article{M85,
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@article {PR04b,
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@book {A68,
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 }

 @book {W84,
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@InProceedings{M93,
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  year = 	"1993",
  editor =	"G. {Di Battista} and P. Eades and H. {de} Fraysseix
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  month =	"26--29~" # sep,
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  publisher =	"Centre D'Analyse et de Math{\'e}matique Sociales,
		 Paris Sorbonne",
}

@Article{EM99,
  author =	"Hikoe Enomoto and Miki Shimabara Miyauchi",
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  year = 	"1999",
  number =	"3",
  volume =	"12",
  editor =	"David B. Shmoys",
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  address =	"Philadelphia, PA",
}

@article {EMK99,
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              Katsuhiro},
     TITLE = {Lower bounds for the number of edge-crossings over the spine
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   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {92},
      YEAR = {1999},
    NUMBER = {2-3},
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       URL = {http://dx.doi.org/10.1016/S0166-218X(99)00044-X},
}
	

@Article{M05,
  title =	"Embedding a Graph into a $d + 1$-page Book with $\lceil m \log_d n\rceil$ Edge-crossings over the Spine",
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  year = 	"2005",
  number =	"5",
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}

@InProceedings{MS08,
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  year = 	"2008",
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  ISBN = 	"978-3-642-00218-2",
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  series =	"Lecture Notes in Computer Science",
}

@InProceedings{BH11,
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}

@book {SU97,
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@article {EGM07,
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@Article{HPSS07,
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  year = 	"2007",
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  volume =	"47",
  pages =	"465--479",
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@article {DEGM05,
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              T. and Meng, Jeremy Y.},
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}

@incollection {BNUW07,
    AUTHOR = {Benkert, Marc and N{\"o}llenburg, Martin and Uno, Takeaki and
              Wolff, Alexander},
     TITLE = {Minimizing intra-edge crossings in wiring diagrams and public
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      YEAR = {2007},
}

@incollection {BKPS08,
    AUTHOR = {Bekos, Michael A. and Kaufmann, Michael and Potika, Katerina
              and Symvonis, Antonios},
     TITLE = {Line crossing minimization on metro maps},
 BOOKTITLE = {Graph drawing},
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      YEAR = {2008},
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@article {ABKS10,
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    NUMBER = {1},
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      ISSN = {1526-1719},
}

@incollection{ABS11,
   author = {Argyriou, Evmorfia and Bekos, Michael and Symvonis, Antonios},
   title = {The Straight-Line {RAC} Drawing Problem Is {NP}-Hard},
   booktitle = {SOFSEM 2011: Theory and Practice of Computer Science},
   series = {Lecture Notes in Computer Science},
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  pages = {74-85},
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   year = {2011}
}

@article {BBBH11,
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}

@Article{B07,
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}

@incollection {MZ99,
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}

@incollection {MZ99b,
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     TITLE = {The constrained crossing minimization problem},
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}

@article {DEKW06,
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@article {DV12,
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@mastersthesis{MC12,
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@incollection {CM10,
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@article {RS05,
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     CODEN = {JGTHDO},
}

@misc{H98w,
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@phdthesis{E73,
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@incollection {G71b,
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      YEAR = {1971},
}

@article {K91,
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      ISSN = {0095-8956},
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@Article{K91b,
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     TITLE = {String graphs. {II}. {R}ecognizing string graphs is {NP}-hard},
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@book {D59,
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@inproceedings{KM09,
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@article {S86,
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@article {BSW83,
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   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
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}

@InProceedings{G89,
  title =	"On Global Wire Ordering for Macro-Cell Routing",
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  year = 	"1989",
  booktitle =	"26th Conference on Design Automation Conference",
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}

@Article{CL98,
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@Article{MS95,
  title =	"The crossing distribution problem",
  author =	"Malgorzata Marek-Sadowska and Majid Sarrafzadeh",
  journal =	"IEEE Trans. on CAD of Integrated Circuits and
		 Systems",
  year = 	"1995",
  number =	"4",
  volume =	"14",
  pages =	"423--433",
}

@techreport{KGB97,
  title={Optimization of Placement Driven by the Cost of Wire Crossing.},
  author={Kapur, N. and Ghosh, D. and Brglez, F.},
  year={1997},
  institution={CBL, North Carolina State University},
  number = {1997-TR@CBL-08-Kapur},
  month = "Oct",
}

@article {S84,
    AUTHOR = {Schumacher, H.},
     TITLE = {Ein {$7$}-{F}arbensatz {$1$}-einbettbarer {G}raphen auf der
              projektiven {E}bene},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t
              Hamburg},
    VOLUME = {54},
      YEAR = {1984},
     PAGES = {5--14},
      ISSN = {0025-5858},
}

@incollection {S90,
    AUTHOR = {Schumacher, H.},
     TITLE = {On {$2$}-embeddable graphs},
 BOOKTITLE = {Topics in combinatorics and graph theory ({O}berwolfach,
              1990)},
     PAGES = {651--661},
 PUBLISHER = {Physica},
   ADDRESS = {Heidelberg},
      YEAR = {1990},
}

@InProceedings{KM08,
  title =	"Minimal Obstructions for 1-Immersions and Hardness of
		 1-Planarity Testing",
  author =	"Vladimir P. Korzhik and Bojan Mohar",
  publisher =	"Springer",
  year = 	"2008",
  volume =	"5417",
  booktitle =	"Graph Drawing",
  editor =	"Ioannis G. Tollis and Maurizio Patrignani",
  ISBN = 	"978-3-642-00218-2",
  pages =	"302--312",
  series =	"Lecture Notes in Computer Science",
}

@article{BJYZ11,
 author = {Bereg, Sergey and Jiang, Minghui and Yang, Boting and Zhu, Binhai},
 title = {On the red/blue spanning tree problem},
 journal = {Theor. Comput. Sci.},
 issue_date = {May, 2011},
 volume = {412},
 issue = {23},
 month = {May},
 year = {2011},
 issn = {0304-3975},
 pages = {2459--2467},
 numpages = {9},
 publisher = {Elsevier Science Publishers Ltd.},
 address = {Essex, UK},
}

@article {BBD09,
    AUTHOR = {Biedl, Therese and Brandenburg, Franz J. and Deng, Xiaotie},
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    VOLUME = {309},
      YEAR = {2009},
    NUMBER = {7},
     PAGES = {1813--1823},
      ISSN = {0012-365X},
}

@article{R65,
    AUTHOR = {Ringel, Gerhard},
     TITLE = {Ein {S}echsfarbenproblem auf der {K}ugel},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"at
              Hamburg},
    VOLUME = {29},
      YEAR = {1965},
     PAGES = {107--117},
      ISSN = {0025-5858},
}

@incollection {R81,
    AUTHOR = {Ringel, G.},
     TITLE = {A nine color theorem for the torus and the {K}lein bottle},
 BOOKTITLE = {The theory and applications of graphs ({K}alamazoo, {M}ich.,
              1980)},
     PAGES = {507--515},
 PUBLISHER = {Wiley},
   ADDRESS = {New York},
      YEAR = {1981},
      ISBN = {0-471-08473-5},
}

@incollection {R64,
    AUTHOR = {Ringel, G.},
     TITLE = {Extremal problems in the theory of graphs},
 BOOKTITLE = {Theory of {G}raphs and its {A}pplications ({P}roc. {S}ympos.
              {S}molenice, 1963)},
     PAGES = {85--90},
 PUBLISHER = {Publ. House Czechoslovak Acad. Sci., Prague},
      YEAR = {1964},
}

@book {W07,
    AUTHOR = {Wallis, W. D.},
     TITLE = {A beginner's guide to graph theory},
   EDITION = {Second},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {2007},
     PAGES = {xx+260},
      ISBN = {978-0-8176-4484-0},
}

@book {ACGKMP99,
    AUTHOR = {Ausiello, G. and Crescenzi, P. and Gambosi, G. and Kann, V.
              and Marchetti-Spaccamela, A. and Protasi, M.},
     TITLE = {Complexity and approximation},
      subtitle = {Combinatorial optimization problems and their approximability
              properties},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1999},
     PAGES = {xx+524},
      ISBN = {3-540-65431-3},
}

@Book{H96,
  editor =	"Dorit S. Hochbaum",
  title =	"Approximation Algorithms for {NP}-Hard Problems",
  publisher =	"PWS Publishing Company, Boston, MA",
  year = 	"1996",
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@book {AB10,
     TITLE = {Algorithms and theory of computation handbook},
    SERIES = {Chapman \& Hall/CRC Applied Algorithms and Data Structures
              Series},
   EDITION = {Second},
    EDITOR = {Atallah, Mikhail J. and Blanton, Marina},
 PUBLISHER = {CRC Press},
   ADDRESS = {Boca Raton, FL},
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     PAGES = {xvi+934},
      ISBN = {978-1-58488-820-8},
}

@book {A06,
    AUTHOR = {Ashlock, Daniel},
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 PUBLISHER = {Springer},
   ADDRESS = {New York},
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}

@InProceedings{B88,
  author =	"Franz J. Brandenburg",
  title =	"Nice Drawings of Graphs are Computationally Hard",
  pages =	"1--15",
  booktitle =	"7th Interdisciplinary Work. Informatics and
		 Psychology",
  year = 	"1988",
  month =	"24--27~" # may,
  location =	"Scharding, Austria",
  publisher =	"Springer-Verlag",
  series =	"Lecture Notes in Computer Science, LNCS",
  volume =	"439",
}

@article {A00,
    AUTHOR = {Alon, Noga},
     TITLE = {Algebraic and probabilistic methods in discrete mathematics},
      NOTE = {GAFA 2000 (Tel Aviv, 1999)},
   JOURNAL = {Geom. Funct. Anal.},
  FJOURNAL = {Geometric and Functional Analysis},
      YEAR = {2000},
    VOLUME = {Special Volume, Part II},
     PAGES = {455--470},
      ISSN = {1016-443X},
}

@incollection{DEGKN11,
   author = {Duncan, Christian and Eppstein, David and Goodrich, Michael and Kobourov, Stephen and N\"{o}llenburg, Martin},
   title = {Lombardi Drawings of Graphs},
   booktitle = {Graph Drawing},
   series = {Lecture Notes in Computer Science},
   editor = {Brandes, Ulrik and Cornelsen, Sabine},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-18468-0},
   pages = {195-207},
   volume = {6502},
   year = {2011}
}

@Article{DEL11,
  title =	"Drawing graphs with right angle crossings",
  author =	"Walter Didimo and Peter Eades and Giuseppe Liotta",
  journal =	"Theor. Comput. Sci",
  year = 	"2011",
  number =	"39",
  volume =	"412",
  pages =	"5156--5166",
}

@article{vK11,
author = "Kreveld, Marc van",
title = "Bold graph drawings",
journal = "Computational Geometry",
volume = "44",
number = "9",
pages = "499 - 506",
year = "2011",
note = "",
issn = "0925-7721",

}

@article {EvKMS09,
    AUTHOR = {Eppstein, David and van Kreveld, Marc and Mumford, Elena and
              Speckmann, Bettina},
     TITLE = {Edges and switches, tunnels and bridges},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {42},
      YEAR = {2009},
    NUMBER = {8},
     PAGES = {790--802},
      ISSN = {0925-7721},
}

%use AFMS12 instead
@misc{AFMS1?,
author = {\'{A}brego, Bernardo M. and Fern\'{a}ndez-Merchant, Silvia  and Salazar, Gelasio},
title = {The rectilinear crossing number of {$K_n$}: Closing in (or are we?)},
note = {Manuscript, 2011.}
}

@incollection{AFMS12,
    author = {\'{A}brego, Bernardo M. and Fern\'{a}ndez-Merchant, Silvia  and Salazar, Gelasio},
    title = {The rectilinear crossing number of {$K_n$}: Closing in (or are we?)},
    booktitle = {Thirty Essays on Geometric Graph Theory},
    publisher = {Springer},
    editor = {Pach, J\'{a}nos},
    pages = {563--567},
    isbn = {978-1-4614-0109-4},
    year = 2012,
}




@article {PR07,
    AUTHOR = {Pan, Shengjun and Richter, R. Bruce},
     TITLE = {The crossing number of {$K_{11}$} is 100},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {56},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {128--134},
      ISSN = {0364-9024},
}

@article {H05,
    AUTHOR = {Ho, Pak Tung},
     TITLE = {The crossing number of {$K_{4,n}$} on the real projective
              plane},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {304},
      YEAR = {2005},
    NUMBER = {1-3},
     PAGES = {23--33},
      ISSN = {0012-365X},
}


@article {RS96,
    AUTHOR = {Richter, R. Bruce and {\v{S}}ir{\'a}{\v{n}}, J.},
     TITLE = {The crossing number of {$K_{3,n}$} in a surface},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {21},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {51--54},
      ISSN = {0364-9024},
}

@article {ESZ06,
    AUTHOR = {Ellingham, M. N. and Stephens, Chris and Zha, Xiaoya},
     TITLE = {The nonorientable genus of complete tripartite graphs},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {96},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {529--559},
      ISSN = {0095-8956},
}

@article {R07b,
    AUTHOR = {Riskin, Adrian},
     TITLE = {The biplanar crossing number of {$C^4_n$}},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {49},
      YEAR = {2007},
     PAGES = {79--85},
      ISSN = {1183-1278},
}

@phdthesis{L09,
    AUTHOR = {Lambert, Joshua K.},
     TITLE = {Determining the biplanar crossing number of {$C_{K} \times C_{L} \times C_{M} \times C_{N}$}},
      school = {North Dakota State University},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2009},
     PAGES = {71},
      ISBN = {978-1109-16712-2},
}

@Article{FG11,
  title =	"On the Orchard crossing number of the complete bipartite graphs {$K_{n,n}$}",
  author =	"Elie Feder and David Garber",
  journal =	"The Electronic Journal of Combinatorics",
  year = 	"2011",
  month = "October",
  volume =	"18",
  issue = "1",
}

@ARTICLE{FG11b,
   author = {{Feder}, Elie and {Garber}, David},
    title = "{On the Orchard crossing number of prisms, ladders and other related graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1111.5412},
        note = {\arxiv{1111.5412} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2011,
    month = nov,
}

@article {FG14,
    AUTHOR = {Feder, Elie and Garber, David},
     TITLE = {On the orchard crossing number of prisms, ladders and other related graphs},
   JOURNAL = {J. Combin. Math. Combin. Comput.},
  FJOURNAL = {Journal of Combinatorial Mathematics and Combinatorial
              Computing},
    VOLUME = {91},
      YEAR = {2014},
     PAGES = {215--232},
      ISSN = {0835-3026},
}

@article {H09,
    AUTHOR = {Ho, Pak Tung},
     TITLE = {The toroidal crossing number of {$K_{4,n}$}},
   JOURNAL = {Discrete Math.},
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    VOLUME = {309},
      YEAR = {2009},
    NUMBER = {10},
     PAGES = {3238--3248},
      ISSN = {0012-365X},
}

@article{U55,
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    journal = {Comptes Rendus},
    publisher = {Soci\'{e}t\'{e} Polonaise de Math\'{e}mathique},
    year = {1955},
    pages = {200--201},
}

@incollection {G69,
    AUTHOR = {Guy, Richard K.},
     TITLE = {The decline and fall of {Z}arankiewicz's theorem},
 BOOKTITLE = {Proof {T}echniques in {G}raph {T}heory ({P}roc. {S}econd {A}nn
              {A}rbor {G}raph {T}heory {C}onf., {A}nn {A}rbor, {M}ich.,
              1968)},
     PAGES = {63--69},
 PUBLISHER = {Academic Press, New York},
      YEAR = {1969},
}

@incollection {HZ95,
    AUTHOR = {Harborth, Heiko and Zahn, Sophie},
     TITLE = {Maximum number of crossings in drawings of small graphs},
 BOOKTITLE = {Graph theory, combinatorics, and algorithms, {V}ol.\ 1, 2 ({K}alamazoo, {MI}, 1992)},
    SERIES = {Wiley-Intersci. Publ.},
     PAGES = {485--495},
 PUBLISHER = {Wiley},
   ADDRESS = {New York},
      YEAR = {1995},
}

@incollection {W71,
    AUTHOR = {Woodall, D. R.},
     TITLE = {Thrackles and deadlock},
 BOOKTITLE = {Combinatorial {M}athematics and its {A}pplications ({P}roc.
              {C}onf., {O}xford, 1969)},
     PAGES = {335--347},
 PUBLISHER = {Academic Press},
   ADDRESS = {London},
      YEAR = {1971},
}

@inproceedings {FHHK10,
    AUTHOR = {Feder, Elie and Harborth, Heiko and Herzberg, Steven and
              Klein, Sheldon},
     TITLE = {The maximum rectilinear crossing number of the {P}etersen
              graph},
 BOOKTITLE = {Proceedings of the {F}orty-{F}irst {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory and {C}omputing},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
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      YEAR = {2010},
     PAGES = {31--40},
      ISSN = {0384-9864},
}

@article {AF07,
    AUTHOR = {{\'A}brego, Bernardo M. and Fern{\'a}ndez-Merchant, Silvia},
     TITLE = {Geometric drawings of {$K_n$} with few crossings},
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  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {114},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {373--379},
      ISSN = {0097-3165},
}




@article {AGOR07,
    AUTHOR = {Aichholzer, Oswin and Garc{\'{\i}}a, Jes{\'u}s and Orden,
              David and Ramos, Pedro},
     TITLE = {New lower bounds for the number of {$(\leq k)$}-edges and the
              rectilinear crossing number of {$K_n$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {38},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {1--14},
      ISSN = {0179-5376},
}


@article {ACFMLS12,
    AUTHOR = {\'Abrego, Bernardo M. and Cetina, Mario and Fern\'{a}ndez-Merchant,
              Silvia and Lea\~nos, Jes\'us and Salazar, Gelasio},
     TITLE = {On {$\leq k$}-edges, crossings, and halving lines of geometric
              drawings of {$K_n$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {48},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {192--215},
      ISSN = {0179-5376},
   MRCLASS = {52C10 (05C62 52C45)},
  MRNUMBER = {2917207},
MRREVIEWER = {T. Thrivikraman},
       DOI = {10.1007/s00454-012-9403-y},
       URL = {http://dx.doi.org/10.1007/s00454-012-9403-y},
}
	

@article {ACFMLS10,
    AUTHOR = {\'{A}brego, Bernardo M. and Cetina, Mario and Fern\'{a}ndez-Merchant, Silvia and
              Lea\~nos,  Jes\'us and Salazar, Gelasio},
     TITLE = {3-symmetric and 3-decomposable geometric drawings of {$K_n$}},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {158},
      YEAR = {2010},
    NUMBER = {12},
     PAGES = {1240--1458},
      ISSN = {0166-218X},
   MRCLASS = {05C62},
  MRNUMBER = {2652001},
MRREVIEWER = {Debra L. Boutin},
       DOI = {10.1016/j.dam.2009.09.020},
       URL = {http://dx.doi.org/10.1016/j.dam.2009.09.020},
}

@article {A86,
    AUTHOR = {Asano, Kouhei},
     TITLE = {The crossing number of {$K_{1,3,n}$} and {$K_{2,3,n}$}},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {10},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {1--8},
      ISSN = {0364-9024},
}

@article {H08,
    AUTHOR = {Ho, Pak Tung},
     TITLE = {The crossing number of {$K_{1,m,n}$}},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {308},
      YEAR = {2008},
    NUMBER = {24},
     PAGES = {5996--6002},
      ISSN = {0012-365X},
}

@article {HZ08,
    AUTHOR = {Huang, Yuanqiu and Zhao, Tinglei},
     TITLE = {The crossing number of {$K_{1,4,n}$}},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {308},
      YEAR = {2008},
    NUMBER = {9},
     PAGES = {1634--1638},
      ISSN = {0012-365X},
}

@article {H11,
    AUTHOR = {Ho, Pak Tung},
     TITLE = {The crossing number of {$K_{1,1,3,n}$}},
   JOURNAL = {Ars Combin.},
  FJOURNAL = {Ars Combinatoria},
    VOLUME = {99},
      YEAR = {2011},
     PAGES = {461--471},
      ISSN = {0381-7032},
}

@MastersThesis{T00,
    author     =     {Christian Th\"{u}rmann},
    title     =     {{Minimale Anzahl von Kanten mit wenigen Kreuzungen in geradlinigen Darstellungen des vollst\"{a}ndigen Graphen}},
    school     =     {{Technischen Universit\"{a}t Braunschweig}},
    address     =     {Germany},
    year     =     {2000},
    }

@inproceedings {H91,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Maximum number of crossings for the cube graph},
 BOOKTITLE = {Proceedings of the {T}wenty-second {S}outheastern {C}onference
              on {C}ombinatorics, {G}raph {T}heory, and {C}omputing ({B}aton
              {R}ouge, {LA}, 1991)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {82},
      YEAR = {1991},
     PAGES = {117--122},
      ISSN = {0384-9864},
}

@inproceedings {HM92,
    AUTHOR = {Harborth, Heiko and Mengersen, Ingrid},
     TITLE = {Drawings of the complete graph with maximum number of
              crossings},
 BOOKTITLE = {Proceedings of the {T}wenty-third {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory, and {C}omputing ({B}oca {R}aton, {FL}, 1992)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {88},
      YEAR = {1992},
     PAGES = {225--228},
      ISSN = {0384-9864},
}

@incollection {HM90,
    AUTHOR = {Harborth, Heiko and Mengersen, Ingrid},
     TITLE = {Edges with at most one crossing in drawings of the complete
              graph},
 BOOKTITLE = {Topics in combinatorics and graph theory ({O}berwolfach,
              1990)},
     PAGES = {757--763},
 PUBLISHER = {Physica, Heidelberg},
      YEAR = {1990},
}

@article {RT97,
    AUTHOR = {Richter, R. Bruce and Thomassen, Carsten},
     TITLE = {Relations between crossing numbers of complete and complete
              bipartite graphs},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {104},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {131--137},
      ISSN = {0002-9890},
}

@article {J71,
    AUTHOR = {Jensen, H. F.},
     TITLE = {An upper bound for the rectilinear crossing number of the
              complete graph},
   JOURNAL = {J. Combinatorial Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {10},
      YEAR = {1971},
     PAGES = {212--216},
}

@article {S64,
    AUTHOR = {Saaty, Thomas L.},
     TITLE = {The minimum number of intersections in complete graphs},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {52},
      YEAR = {1964},
     PAGES = {688--690},
      ISSN = {0027-8424},
}

@article {HKS73,
    AUTHOR = {Harary, Frank and Kainen, Paul C. and Schwenk, Allen J.},
     TITLE = {Toroidal graphs with arbitrarily high crossing numbers},
   JOURNAL = {Nanta Math.},
  FJOURNAL = {Nanyang University. Nanta Mathematica},
    VOLUME = {6},
      YEAR = {1973},
    NUMBER = {1},
     PAGES = {58--67},
      ISSN = {0077-2739},
}

@article {K69,
    AUTHOR = {Koman, Milan},
     TITLE = {On the crossing numbers of graphs},
   JOURNAL = {Acta Univ. Carolinae--Math. et Phys.},
    VOLUME = {10},
      YEAR = {1969},
    NUMBER = {nos. 1--2},
     PAGES = {9--46},
}

@incollection {K75,
    AUTHOR = {Koman, Milan},
     TITLE = {A note on the crossing number of {$K_{m,n}$} on the {K}lein
              bottle},
 BOOKTITLE = {Recent advances in graph theory ({P}roc. {S}econd
              {C}zechoslovak {S}ympos., {P}rague, 1974)},
     PAGES = {327--334},
 PUBLISHER = {Academia},
   ADDRESS = {Prague},
      YEAR = {1975},
}

@article {K78,
    AUTHOR = {Koman, Milan},
     TITLE = {New upper bounds for the crossing number of {$K_{n}$} on the
              {K}lein bottle},
   JOURNAL = {\v Casopis P\v est. Mat.},
  FJOURNAL = {\v Ceskoslovensk\'a Akademie V\v ed. \v Casopis Pro P\v
              estov\'an\'\i \ Matematiky},
    VOLUME = {103},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {282--288},
      ISSN = {0008-7394},
}

@article {K70b,
    AUTHOR = {Koman, Milan},
     TITLE = {Extremal crossing numbers of complete {$k$}-chromatic graphs},
   JOURNAL = {Mat. \v Casopis Sloven. Akad. Vied},
  FJOURNAL = {Matematicky \v Casopis Slovenskej Akad\'emie Vied},
    VOLUME = {20},
      YEAR = {1970},
     PAGES = {315--325},
      ISSN = {0025-5173},
}

%updated to Czech
incollection {BK70,
    AUTHOR = {Bla{\v{z}}ek, Jaroslav and Koman, Milan},
     TITLE = {The number of intersection points of complete {$k$}-chromatic
              graphs},
 BOOKTITLE = {Mathematics ({G}eometry and {G}raph {T}heory) ({C}zech)},
     PAGES = {69--84},
 PUBLISHER = {Univ. Karlova, Prague},
      YEAR = {1970},
}

@incollection {G71,
    AUTHOR = {Guy, Richard K.},
     TITLE = {Unsolved combinatorial problems},
 BOOKTITLE = {Combinatorial {M}athematics and its {A}pplications ({P}roc.
              {C}onf., {O}xford, 1969)},
     PAGES = {121--127},
 PUBLISHER = {Academic Press},
   ADDRESS = {London},
      YEAR = {1971},
   MRCLASS = {05.00},
  MRNUMBER = {0277393 (43 \#3126)},
}

@article {RS01,
    AUTHOR = {Richter, R. Bruce and Salazar, Gelasio},
     TITLE = {The crossing number of {$C_6\times C_n$}},
   JOURNAL = {Australas. J. Combin.},
  FJOURNAL = {The Australasian Journal of Combinatorics},
    VOLUME = {23},
      YEAR = {2001},
     PAGES = {135--143},
      ISSN = {1034-4942},
}

@article{AR04,
author = "Adamsson, Jay and Richter, R. Bruce",
title = "Arrangements, circular arrangements and the crossing number of {$C_7 \times C_n$}",
journal = "Journal of Combinatorial Theory, Series B",
volume = "90",
number = "1",
pages = "21---39",
year = "2004",
issn = "0095-8956",
}

@incollection {T95a,
    AUTHOR = {Thomassen, Carsten},
     TITLE = {Embeddings and minors},
 BOOKTITLE = {Handbook of combinatorics, {V}ol.\ 1},
     PAGES = {301--349},
 PUBLISHER = {Elsevier},
   ADDRESS = {Amsterdam},
      YEAR = {1995},
}

%use dKP12
@ARTICLE{dKP11,
   author = {{de Klerk}, Etienne  and Pasechnik, Dmitrii V.},
    title = "{Improved lower bounds for the $2$-page crossing numbers of {$K_{m,n}$} and {$K_n$} via semidefinite programming}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1110.4824},
  note = {\arxiv{1110.4824} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2011,
    month = oct,
}

@article{dKP12,
author = {{de Klerk}, Etienne  and Pasechnik, Dmitrii V.},
title = {Improved Lower Bounds for the $2$-Page Crossing Numbers of {$K_{m,n}$} and {$K_n$} via Semidefinite Programming},
journal = {SIAM Journal on Optimization},
volume = {22},
number = {2},
pages = {581-595},
year = {2012},
doi = {10.1137/110852206},

URL = {http://epubs.siam.org/doi/abs/10.1137/110852206},
eprint = {http://epubs.siam.org/doi/pdf/10.1137/110852206}
}

@article {dKMPRS06,
    AUTHOR = {{de Klerk}, Etienne  and Maharry, John and Pasechnik, Dmitrii V. and Richter,
              R. Bruce and Salazar, Gelasio},
     TITLE = {Improved bounds for the crossing numbers of {$K_{m,n}$} and
              {$K_n$}},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {20},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {189--202},
      ISSN = {0895-4801},
}

@Article{dKPS07,
  title =	"Reduction of symmetric semidefinite programs using the
		 regular *-representation",
  author =	"de Klerk, Etienne  and Pasechnik, Dmitrii V. and
		 Schrijver, Alexander ",
  journal =	"Math. Program",
  year = 	"2007",
  number =	"2-3",
  volume =	"109",
}

@incollection {HLLT03,
    AUTHOR = {Harvey, Nicholas J. A. and Ladner, Richard E. and Lov{\'a}sz,
              L{\'a}szl{\'o} and Tamir, Tami},
     TITLE = {Semi-matchings for bipartite graphs and load balancing},
 BOOKTITLE = {Algorithms and data structures},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2748},
     PAGES = {294--306},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
}

@article {T88,
    AUTHOR = {Thomassen, Carsten},
     TITLE = {Rectilinear drawings of graphs},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {12},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {335--341},
      ISSN = {0364-9024},
     CODEN = {JGTHDO},
   MRCLASS = {05C10},
  MRNUMBER = {956195 (89i:05111)},
MRREVIEWER = {Joan Hutchinson},
       DOI = {10.1002/jgt.3190120306},
       URL = {http://dx.doi.org/10.1002/jgt.3190120306},
}

@misc{T11,
author = "Carsten Thomassen",
howpublished = "Personal communication",
month = "November",
year = 2011
}

@misc{K14,
 author = "Paul Kainen",
 howpublished  = "Personal communication",
 month = "August",
 year = "2014",
}

@incollection {B97,
    AUTHOR = {Beineke, Lowell W.},
     TITLE = {Topology},
 BOOKTITLE = {Graph connections},
    SERIES = {Oxford Lecture Ser. Math. Appl.},
    VOLUME = {5},
     PAGES = {155--175},
 PUBLISHER = {Oxford Univ. Press},
   ADDRESS = {New York},
      YEAR = {1997},
}

@book {G00,
    AUTHOR = {Gau{\ss}, Carl Friedrich},
     TITLE = {Werke. {B}and {VIII}},
 PUBLISHER = {B.G. Teubner},
   ADDRESS = {Leipzig},
      YEAR = {1900},
     PAGES = {viii+458},
}

@inproceedings{AOR06,
  title={On the structure of sets attaining the rectilinear crossing number},
  author={Aichholzer, Oswin and Orden, David and Ramos, Pedro~A},
  booktitle={Proc. 22nd European Workshop on Computational Geometry EuroCG},
  volume={6},
  pages={43--46},
  year={2006}
}


@ARTICLE{LLRIRM14,
   author = {Lea{\~n}os, Jes\'{u}s and Lomeli, Mario and Ram{\'{\i}}rez-Ib{\'a}{\~n}ez, Marcelino and
	Rivera-Mart{\'{\i}}nez, Luis~Manuel},
    title = "{The second convex hull of every optimal rectilinear drawing of $K_n$ is a triangle}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1411.1699},
  note = {\arxiv{1411.1699} (last accessed 9/21/2017)},
 primaryClass = "math.MG",
 keywords = {Mathematics - Metric Geometry, Mathematics - Combinatorics, 05C10, 68R10},
     year = 2014,
    month = nov,
}

@article {BLPRS07,
    AUTHOR = {Balogh, J{\'o}zsef and Lea{\~n}os, Bernardo M. and Pan, Shengjun and Richter, R. Bruce and Salazar, Gelasio},
     TITLE = {The convex hull of every optimal pseudolinear drawing of
              {$K_n$} is a triangle},
   JOURNAL = {Australas. J. Combin.},
  FJOURNAL = {The Australasian Journal of Combinatorics},
    VOLUME = {38},
      YEAR = {2007},
     PAGES = {155--162},
      ISSN = {1034-4942},
}

@MastersThesis{P06,
  title =	"On the Crossing Numbers of Complete Graphs",
  author =	"Shengjun Pan",
  year = 	"2006",
  school =	"University of Waterloo",
}

@MISC{ABFMLS06,
    AUTHOR = {{\'A}brego, Bernardo M. and Balogh, J{\'o}zsef and Fern{\'a}ndez-Merchant,
              Silvia and Lea{\~n}os, Bernardo M. and Salazar, Gelasio},
    title = {On $(\leq k)$-pseudoedges in generalized configurations and the pseudolinear crossing number of {$K_n$}},
    note = {Submitted.},
    year = {2006}
}

@inProceedings{AFMLS03,
    author = {{\'A}brego, Bernardo M. and Fern{\'a}ndez-Merchant, Silvia and Lea{\~n}os, Jes\'{u}s and Salazar, Gelasio},
    title = {Recent developments on the number of $(\leq k)$-sets, halving lines,
         and the rectilinear crossing number of {$K_n$}},
     booktitle = {Proceedings of the XII Encuentros de Geometr{\'i}a Computacional},
    year = {2007},
    address = "Universidad de Valladolid, Spain",
    isbn = {978-84-690-6900-4},
}

@incollection {AFMLS08,
    AUTHOR = {{\'A}brego, Bernardo M. and Fern{\'a}ndez-Merchant, Silvia and
              Lea{\~n}os, Jes{\'u}s and Salazar, Gelasio},
     TITLE = {The maximum number of halving lines and the rectilinear
              crossing number of {$K_n$} for {$n\le27$}},
 BOOKTITLE = {The {IV} {L}atin-{A}merican {A}lgorithms, {G}raphs, and
              {O}ptimization {S}ymposium},
    SERIES = {Electron. Notes Discrete Math.},
    VOLUME = {30},
     PAGES = {261--266},
 PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
      YEAR = {2008},
}

@article {ABFMLS08,
    AUTHOR = {{\'A}brego, Bernardo M. and Balogh, J{\'o}zsef and Fern{\'a}ndez-Merchant,
              Silvia and Lea{\~n}os, Bernardo M. and Salazar, Gelasio},
     TITLE = {An extended lower bound on the number of {$(\leq k)$}-edges to
              generalized configurations of points and the pseudolinear
              crossing number of {$K_n$}},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {115},
      YEAR = {2008},
    NUMBER = {7},
     PAGES = {1257--1264},
      ISSN = {0097-3165},
}

@incollection {SV99,
    AUTHOR = {Shahrokhi, Farhad and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {On $3$-layer crossings and pseudo arrangements},
 BOOKTITLE = {Graph drawing (\v {S}ti\v r\'\i n {C}astle, 1999)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1731},
     PAGES = {225--231},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1999},
}

@article {SSSV00,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, Ondrej and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {A new lower bound for the bipartite crossing number with
              applications},
      NOTE = {Algorithms for future technologies (Saarbr{\"u}cken, 1997)},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {245},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {281--294},
      ISSN = {0304-3975},
}

@article {SSSV01,
    AUTHOR = {Shahrokhi, Farhad and S{\'y}kora, Ondrej and Sz{\'e}kely,
              L{\'a}szl{\'o} A. and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {On bipartite drawings and the linear arrangement problem},
   JOURNAL = {SIAM J. Comput.},
  FJOURNAL = {SIAM Journal on Computing},
    VOLUME = {30},
      YEAR = {2001},
    NUMBER = {6},
     PAGES = {1773--1789},
      ISSN = {0097-5397},
       DOI = {10.1137/S0097539797331671},
       URL = {http://dx.doi.org/10.1137/S0097539797331671},
}

@article{LM69,
author="Leclerc, B. and Monjardet, B.",
title="{Probl\`{e}mes ouverts. Repr\'{e}sentation graphique d'un graphe.}",
language="French",
journal="Math. et Sci. humaines ",
volume="26",
pages="51-57",
year="1969",
}

@Book{B10,
  title =	"Semiology of Graphics - Diagrams, Networks, Maps",
  author =	"Jacques Bertin",
  publisher =	"ESRI",
  year = 	"2010",
  pages = "xv+438",
  ISBN = 	"978-1-58948-261-6",
  note = {This book was originally published in French in 1967; this translation is based on the second edition from 1974.},
}


@inproceedings{ADBFJKPR10,
 author = {Angelini, Patrizio and Di Battista, Giuseppe and Frati, Fabrizio and Jel\'{\i}nek, V\'{\i}t and Kratochv\'{\i}l, Jan and Patrignani, Maurizio and Rutter, Ignaz},
 title = {Testing planarity of partially embedded graphs},
 booktitle = {Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms},
 series = {SODA '10},
 year = {2010},
 isbn = {978-0-898716-98-6},
 location = {Austin, Texas},
 pages = {202--221},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA},
}

%same as above, different label
@InProceedings{ABFJKPR10,
 author = {Angelini, Patrizio and Di Battista, Giuseppe and Frati, Fabrizio and Jel\'{\i}nek, V\'{\i}t and Kratochv\'{\i}l, Jan and Patrignani, Maurizio and Rutter, Ignaz},
 title = {Testing planarity of partially embedded graphs},
 booktitle = {Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms},
 series = {SODA '10},
 year = {2010},
 isbn = {978-0-898716-98-6},
 location = {Austin, Texas},
 pages = {202--221},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA},
}

@incollection {ADBFPR11,
   author = {Angelini, Patrizio and Di Battista, Giuseppe and Frati, Fabrizio and Patrignani, Maurizio and Rutter, Ignaz},
   affiliation = {Dipartimento di Informatica e Automazione, Università Roma Tre, Italy},
   title = {Testing the Simultaneous Embeddability of Two Graphs Whose Intersection Is a Biconnected Graph or a Tree},
   booktitle = {Combinatorial Algorithms},
   series = {Lecture Notes in Computer Science},
   editor = {Iliopoulos, Costas and Smyth, William},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-19221-0},
   keyword = {Computer Science},
   pages = {212-225},
   volume = {6460},
   year = {2011}
}

@book {DDR08,
     TITLE = {A lifetime of puzzles},
    EDITOR = {Demaine, Erik D. and Demaine, Martin L. and Rodgers, Tom},
      subtitle = {A collection of puzzles in honor of Martin Gardner's 90th
              birthday},
 PUBLISHER = {A K Peters Ltd.},
   ADDRESS = {Wellesley, MA},
      YEAR = {2008},
     PAGES = {x+349},
      ISBN = {978-1-56881-245-8},
}

@article {CGO11,
    AUTHOR = {Chalopin, J{\'e}r{\'e}mie and Gon{\c{c}}alves, Daniel and
              Ochem, Pascal},
     TITLE = {Planar graphs have 1-string representations},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {43},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {626--647},
      ISSN = {0179-5376},
}

@InProceedings{CG09,
  title =	"Every planar graph is the intersection graph of
		 segments in the plane: extended abstract",
  author =	"J{\'e}r{\'e}mie Chalopin and Daniel Gon{\c c}alves",
  booktitle =	"{STOC}",
  publisher =	"ACM",
  year = 	"2009",
  editor =	"Michael Mitzenmacher",
  ISBN = 	"978-1-60558-506-2",
  pages =	"631--638",

}

@TechReport{ES75,
  author =	"S. Even and Y. Shiloah",
  title =	"{NP}-completeness of several arrangement problems",
  institution =  "Technion, Israel Institute of Technology",
  year = 	"1975",
  month = "January",
  number =	"43",
  address =	"Haifa, Israel",
}

@article {MR08,
    AUTHOR = {Ma, Dengju and Ren, Han},
     TITLE = {The projective plane crossing numbers of circular graphs},
   JOURNAL = {J. Syst. Sci. Complex.},
  FJOURNAL = {Journal of Systems Science \& Complexity},
    VOLUME = {21},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {316--322},
      ISSN = {1009-6124},
}

@article {GMS01,
    AUTHOR = {Garcia-Moreno, Enrique and Salazar, Gelasio},
     TITLE = {Bounding the crossing number of a graph in terms of the
              crossing number of a minor with small maximum degree},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {36},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {168--173},
      ISSN = {0364-9024},
}

@inproceedings{CDHK11,
year={2011},
isbn={978-3-642-25010-1},
booktitle={Combinatorial Algorithms},
volume={7056},
series={Lecture Notes in Computer Science},
editor={Iliopoulos, Costas S. and Smyth, William F.},
title={How Not to Characterize Planar-Emulable Graphs},
publisher={Springer},
address = {Berlin},
author={Chimani, Markus and Derka, Martin and Hlin{\v{e}}ny, Petr and Klus\'{a}\v{c}ek, Mat\v{e}j},
pages={106-120}
}

%use ADLDBFMR15
@article{ADLDBFR12,
  author    = {Patrizio Angelini and
               Giordano Da Lozzo and
               Giuseppe Di Battista and
               Fabrizio Frati and
               Vincenzo Roselli},
  title     = {Beyond Clustered Planarity},
  journal   = {CoRR},
  volume    = {abs/1207.3934},
  year      = {2012},
  ee        = {http://arxiv.org/abs/1207.3934},
}

%use ADLDBFMR15
@ARTICLE{ADLDBFMR12,
  author    = {Patrizio Angelini and
               Giordano Da Lozzo and
               Giuseppe Di Battista and
               Fabrizio Frati and
               Patrignani, Maurizio,
               Vincenzo Roselli},
    title = "{Relaxing the Constraints of Clustered Planarity}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1207.3934},
  note = {\arxiv{1207.3934} (last accessed 9/21/2017)},
 primaryClass = "cs.DM",
 keywords = {Computer Science - Discrete Mathematics, Computer Science - Computational Geometry},
     year = 2012,
    month = jul,
   adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1207.3934A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {ADLDBFMR15,
    AUTHOR = {Angelini, Patrizio and Da Lozzo, Giordano and Di Battista,
              Giuseppe and Frati, Fabrizio and Patrignani, Maurizio and
              Roselli, Vincenzo},
     TITLE = {Relaxing the constraints of clustered planarity},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {48},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {42--75},
      ISSN = {0925-7721},
   MRCLASS = {05C62 (68R10)},
  MRNUMBER = {3260247},
MRREVIEWER = {Bin Liu},
       DOI = {10.1016/j.comgeo.2014.08.001},
       URL = {http://dx.doi.org/10.1016/j.comgeo.2014.08.001},
}


@article {H03,
    AUTHOR = {Hlin{\v{e}}ny, Petr},
     TITLE = {Crossing-number critical graphs have bounded path-width},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {88},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {347--367},
      ISSN = {0095-8956},
}

@InProceedings{M09b,
  title =	"The Crossing Number of Graphs: Theory and
		 Computation",
  author =	"Petra Mutzel",
  booktitle =	"Efficient Algorithms",
  publisher =	"Springer",
  year = 	"2009",
  volume =	"5760",
  editor =	"Susanne Albers and Helmut Alt and Stefan N{\"a}her",
  ISBN = 	"978-3-642-03455-8",
  pages =	"305--317",
  series =	"Lecture Notes in Computer Science",
}

@article {B95,
    AUTHOR = {Borodin, Oleg V.},
     TITLE = {A new proof of the {$6$} color theorem},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {19},
      YEAR = {1995},
    NUMBER = {4},
     PAGES = {507--521},
      ISSN = {0364-9024},
}

@article {T77,
author = {Tur\'{a}n, Paul},
title = {A note of welcome},
journal = {Journal of Graph Theory},
volume = {1},
number = {1},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1097-0118},
pages = {7--9},
year = {1977},
}

@article {Z53,
    AUTHOR = {Zarankiewicz, K.},
     TITLE = {The solution of a certain problem on graphs of {P}. {T}uran},
   JOURNAL = {Bull. Acad. Polon. Sci. Cl. III.},
    VOLUME = {1},
      YEAR = {1953},
     PAGES = {167--168},
}

@mastersthesis{P12,
    author = {Pierobon, Marco},
    title = {Minimization of the Crossing Number in a Reconciled Tree},
    school = {Universit\'{a} deglie Studi di Padova},
    address = {Padua, Italy},
    year = {2012},
}

@article {M01,
    AUTHOR = {Mutzel, Petra},
     TITLE = {An alternative method to crossing minimization on hierarchical
              graphs},
   JOURNAL = {SIAM J. Optim.},
  FJOURNAL = {SIAM Journal on Optimization},
    VOLUME = {11},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {1065--1080},
      ISSN = {1052-6234},
}

@misc{S71,
 author = "David A. Singer",
 title = "The Rectilinear Crossing Number of Certain Graphs",
 note = "Manuscript at \url{http://www.cwru.edu/artsci/math/singer/publish/Rectilinear_crossings.pdf} (last accessed 1/9/2013)",
 year = "1971",
}

@Article{P02,
  title =	"Metrics for Graph Drawing Aesthetics",
  author =	"Helen C. Purchase",
  journal =	"J. Vis. Lang. Comput",
  year = 	"2002",
  number =	"5",
  volume =	"13",
  pages =	"501--516",
}

@inbook{P04a,
    Author = {Purchase, Helen C.},
	Pages = {145-178},
	Title = {Computer Graphics and Multimedia: Applications, Problems and Solutions},
    Chapter = {Evaluating Graph Drawing Aesthetics: defining and exploring a new empirical research area},
    Publisher = {Idea Group Publishing},
    Year = {2004}}

@article{H08a,
  author    = {Weidong Huang},
  title     = {An Eye Tracking Study into the Effects of Graph Layout},
  journal   = {CoRR},
  volume    = {abs/0810.4431},
  year      = {2008},
  ee        = {http://arxiv.org/abs/0810.4431},
    note = {\arxiv{0810.4431} (last accessed 9/21/2017)},
}

@article {ST02,
    AUTHOR = {Spencer, Joel and T{\'o}th, G{\'e}za},
     TITLE = {Crossing numbers of random graphs},
      NOTE = {Random structures and algorithms (Poznan, 2001)},
   JOURNAL = {Random Structures Algorithms},
  FJOURNAL = {Random Structures \& Algorithms},
    VOLUME = {21},
      YEAR = {2002},
    NUMBER = {3-4},
     PAGES = {347--358},
      ISSN = {1042-9832},
}

@article {PRTT06,
    AUTHOR = {Pach, J{\'a}nos and Radoi{\v{c}}i{\'c}, Rado{\v{s}} and
              Tardos, G{\'a}bor and T{\'o}th, G{\'e}za},
     TITLE = {Improving the crossing lemma by finding more crossings in
              sparse graphs},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {36},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {527--552},
      ISSN = {0179-5376},
}

@article {HSM10,
    AUTHOR = {He, Hongmei and S{\u{a}}l{\u{a}}gean, Ana and M{\"a}kinen,
              Erkki},
     TITLE = {One- and two-page crossing numbers for some types of graphs},
   JOURNAL = {Int. J. Comput. Math.},
  FJOURNAL = {International Journal of Computer Mathematics},
    VOLUME = {87},
      YEAR = {2010},
    NUMBER = {8},
     PAGES = {1667--1679},
      ISSN = {0020-7160},
}

@InProceedings{FHSV05,
  title =	"Outerplanar Crossing Numbers of 3-Row Meshes, {H}alin
		 Graphs and Complete p-Partite Graphs",
  author =	"Fulek, Radoslav  and He, Hongmei  and S{\'y}kora, Ondrej
		 and V{\v{r}}{\v{t}}o, Imrich ",
  booktitle =	"{SOFSEM} 2005: Theory and Practice of Computer
		 Science, 31st Conference on Current Trends in Theory
		 and Practice of Computer Science, Liptovsk{\'y}
		 {J}{\'a}n, Slovakia, January 22-28, 2005, Proceedings",
  publisher =	"Springer",
  year = 	"2005",
  volume =	"3381",
  editor =	"Peter Vojt{\'a}s and M{\'a}ria Bielikov{\'a} and
		 Bernadette Charron-Bost and Ondrej S{\'y}kora",
  ISBN = 	"3-540-24302-X",
  pages =	"376--379",
  series =	"Lecture Notes in Computer Science",
 }

 @article {GH73,
    AUTHOR = {Guy, Richard K. and Hill, Anthony},
     TITLE = {The crossing number of the complement of a circuit},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {5},
      YEAR = {1973},
     PAGES = {335--344},
      ISSN = {0012-365X},
}

@article {KRS96,
    AUTHOR = {Kle{\v{s}}{\v{c}}, Mari{\'a}n and Richter, R. Bruce and
              Stobert, Ian},
     TITLE = {The crossing number of {$C_5\times C_n$}},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {22},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {239--243},
      ISSN = {0364-9024},
}

@InProceedings{HHE08,
  title =	"Effects of Crossing Angles",
  author =	"Huanh, Weidong and Hong, Seok-Hee and Eaders, Peter",
  publisher =	"IEEE",
  year = 	"2008",
  booktitle =	"PacificVis",
  pages =	"41--46",
}

@Article{DGMW11,
  author="Vida Dujmovi{\'c} and Joachim Gudmundsson and Pat Morin and Thomas Wolle",
  title="Notes on large angle crossing graphs",
  journal={Chicago Journal of Theoretical Computer Science},
  volume={2011},
  number={4},
  publisher={University of Chicago},
  month={June},
  year={2011}
}





@InProceedings{GSM10,
  title =	"Optimal $k$-Level Planarization and Crossing
		 Minimization",
  author =	"Graeme Gange and Peter J. Stuckey and Kim Marriott",
  publisher =	"Springer",
  year = 	"2010",
  volume =	"6502",
  booktitle =	"Graph Drawing",
  editor =	"Ulrik Brandes and Sabine Cornelsen",
  ISBN = 	"978-3-642-18468-0",
  pages =	"238--249",
  series =	"Lecture Notes in Computer Science",
}

@article {DGDLM11,
    AUTHOR = {Di Giacomo, Emilio and Didimo, Walter and Liotta, Giuseppe and
              Meijer, Henk},
     TITLE = {Area, curve complexity, and crossing resolution of non-planar
              graph drawings},
   JOURNAL = {Theory Comput. Syst.},
  FJOURNAL = {Theory of Computing Systems},
    VOLUME = {49},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {565--575},
      ISSN = {1432-4350},
}


@InProceedings{N89,
 author = {Newbery, Frances J.},
 title = {Edge concentration: a method for clustering directed graphs},
 booktitle = {Proceedings of the 2nd International Workshop on Software configuration management},
 series = {SCM '89},
 year = {1989},
 isbn = {0-89791-334-5},
 location = {Princeton, New Jersey, United States},
 pages = {76--85},
 publisher = {ACM},
 address = {New York, NY, USA},
}

@InProceedings{PNK10,
  title =	"Improving Layered Graph Layouts with Edge~Bundling",
  author =	"Pupyrev, Sergey and Nachmanson, Lev and Kaufmann, Michael",
  publisher =	"Springer",
  year = 	"2010",
  volume =	"6502",
  booktitle =	"Graph Drawing",
  editor =	"Ulrik Brandes and Sabine Cornelsen",
  ISBN = 	"978-3-642-18468-0",
  pages =	"329--340",
  series =	"Lecture Notes in Computer Science",
}

@article{H06b,
  author    = {Danny Holten},
  title     = {Hierarchical Edge Bundles: Visualization of Adjacency Relations in
               Hierarchical Data},
  journal   = {{IEEE} Trans. Vis. Comput. Graph.},
  volume    = {12},
  number    = {5},
  pages     = {741--748},
  year      = {2006},
  url       = {https://doi.org/10.1109/TVCG.2006.147},
  doi       = {10.1109/TVCG.2006.147},
  timestamp = {Sun, 28 May 2017 13:18:28 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/tvcg/Holten06},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@misc{I08,
  author = {Kazumasa Ishiguro},
  title = {The minimum non-crossing edge number of graphs},
  year = {2008},
  address = {Yokohama National University, Japan},
  howpublished = {Talk at $20$th Workshop on Topological Graph Theory, Yokohama National University, Japan},
  url = {http://www.ngm.ed.ynu.ac.jp/negami/tgt/tgt20/abstract/ishiguro_tgt20.pdf},
}

%use A15
@unpublished{A13b,
  author = {Eyal Ackerman},
  title = {On topological graphs with at most four crossings per edge},
  year = 2013,
  address = {University of Haifa, Israel},
  note = {Unpublished manuscript at \url{http://sci.haifa.ac.il/~ackerman/publications/4crossings.pdf}},
}

%use A19
@ARTICLE{A15,
   author = {{Ackerman}, Eyal},
    title = "{On topological graphs with at most four crossings per edge}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1509.01932},
  note = {\arxiv{1509.01932} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Computational Geometry},
     year = 2015,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150901932A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {A19,
    AUTHOR = {Ackerman, Eyal},
     TITLE = {On topological graphs with at most four crossings per edge},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {85},
      YEAR = {2019},
     PAGES = {101574, 31},
      ISSN = {0925-7721},
   MRCLASS = {05C10 (05C62)},
  MRNUMBER = {4010251},
       DOI = {10.1016/j.comgeo.2019.101574},
       URL = {https://doi.org/10.1016/j.comgeo.2019.101574},
}

@incollection {GH99,
    AUTHOR = {Gavoille, Cyril and Hanusse, Nicolas},
     TITLE = {Compact routing tables for graphs of bounded genus (extended
              abstract)},
 BOOKTITLE = {Automata, languages and programming ({P}rague, 1999)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1644},
     PAGES = {351--360},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1999},
}

@article {D36,
    AUTHOR = {Dehn, M.},
     TITLE = {\"{U}ber kombinatorische {T}opologie},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {67},
      YEAR = {1936},
    NUMBER = {1},
     PAGES = {123--168},
      ISSN = {0001-5962},
}

@article {K11,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {Outerplanar crossing numbers of planar graphs},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {61},
      YEAR = {2011},
     PAGES = {69--76},
      ISSN = {1183-1278},
}

@inproceedings{Y86,
 author = {Yannakakis, Mihalis},
 title = {Four pages are necessary and sufficient for planar graphs},
 booktitle = {Proceedings of the eighteenth annual ACM symposium on Theory of computing},
 series = {STOC '86},
 year = {1986},
 isbn = {0-89791-193-8},
 location = {Berkeley, California, United States},
 pages = {104--108},
 numpages = {5},
 publisher = {ACM},
 address = {New York, NY, USA},
}

@article {Y89,
    AUTHOR = {Yannakakis, Mihalis},
     TITLE = {Embedding planar graphs in four pages},
      NOTE = {18th Annual ACM Symposium on Theory of Computing (Berkeley,
              CA, 1986)},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {38},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {36--67},
      ISSN = {0022-0000},
}


@article{HEHL12,
title = "Improving multiple aesthetics produces better graph drawings",
journal = "Journal of Visual Languages \&\ Computing",
volume = "",
number = "",
pages = "",
year = "2012",
issn = "1045-926X",
author = "Huang, Weidong  and Eades, Peter  and Hong, Seok-Hee  and Lin,  Chun-Cheng",
}

@conference{HHL12,
title = "Evaluating Force-Directed Algorithms with a New Framework",
booktitle= "27th ACM Symposium on Applied Computing",
year = "2012",
author = "Huang, Maolin and Huang, Weidong and Lin,  Chun-Cheng",
}


@inproceedings{B1885,
author = {Baltzer, R},
title = {Eine {E}rinnerung an {M\"{o}bius} und seinen {F}reund {W}eiske},
booktitle = "Berichte {\"{u}}ber die Verhandlungen der K{\"{o}}niglich S{\"{a}}chsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-Physische Classe.",
volume = {37},
pages = {1--6},
publisher = {S. Hirzel},
address = {Leipzig},
year = {1885},
}

@book{K1889,
  title={Lehrbuch der ebenen {E}lementar-{G}eometrie ({P}lanimetrie)},
  author={Kleyer, A. and Sachs, J.},
  year={1889},
  publisher={J. Maier}
}

@book{S1893,
  title={Lehrbuch der Kombinatorik},
  author={Staudacher, H.},
  year={1893},
  publisher={J. Maier}
}

@article{T1877,
  title={Some elementary properties of closed plane curves},
  author={Tait, Peter Guthrie},
  journal={Messenger of Mathematics},
  pages={132--133},
  publisher = "MacMillan",
  year={1877}
}

@article {WRX11,
    AUTHOR = {Wu, Yong Xiang and Ren, Han and Xu, Tu},
     TITLE = {The crossing number of two-maps on orientable surfaces},
   JOURNAL = {J. Math. Res. Exposition},
  FJOURNAL = {Journal of Mathematical Research and Exposition},
    VOLUME = {31},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {643--648},
      ISSN = {1000-341X},
}

%use C13
@ARTICLE{C12,
   author = {Cabello, Sergio},
    title = "{Hardness of approximation for crossing number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1204.0660},
     note = {\arxiv{1204.0660} (last accessed 9/21/2017)},
 primaryClass = "cs.CG",
    year = 2012,
    month = apr,
}

@article {C13,
    AUTHOR = {Cabello, Sergio},
     TITLE = {Hardness of {A}pproximation for {C}rossing {N}umber},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {49},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {348--358},
      ISSN = {0179-5376},
}



@inproceedings{W01,
  title =	"Graph Layout for Displaying Data Structures",
  author =	"Vance Waddle",
  booktitle =	"Graph Drawing",
  publisher =	"Springer",
  year = 	"2000",
  volume =	"1984",
  month =	jan # "~01",
  editor =	"Joe Marks",
  ISBN = 	"3-540-41554-8",
  pages =	"241--252",
  series =	"Lecture Notes in Computer Science",
}

@inproceedings{KSSH12,
  author = {Lars Kristian Klauske and Christoph Daniel Schulze and Miro Sp{\"o}nemann and Reinhard von Hanxleden},
  title = {Improved Layout for Data Flow Diagrams with Port Constraints},
  booktitle = {Proceedings of the 7th International Conference on the Theory and Application of Diagrams (DIAGRAMS'12)},
  publisher = {Springer},
  series = {LNCS},
  year = {2012},
}

@InProceedings{KMBW01,
  title =	"A Short Note on the History of Graph Drawing",
  author =	"Kruja, Eriola and Marks, Joe and Blair, Ann and Waters, Richard
		 C.",
  publisher =	"Springer",
  year = 	"2001",
  volume =	"2265",
  booktitle =	"Graph Drawing",
  editor =	"Petra Mutzel and Michael J{\"u}nger and Sebastian
		 Leipert",
  ISBN = 	"3-540-43309-0",
  pages =	"272--286",
  series =	"Lecture Notes in Computer Science",
}

@book{B09,
  title={Mathematical works printed in the Americas, 1554-1700},
  author={Burdick, B.S.},
  year={2009},
  isbn = "0-8018-8823-9",
  publisher={John Hopkins University Press}
}

@ARTICLE{BR12,
   author = {{Bl{\"a}sius}, T. and {Rutter}, I.},
    title = "{Disconnectivity and Relative Positions in Simultaneous Embeddings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1204.2903},
    note = {\arxiv{1204.2903} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
     year = 2012,
    month = apr,
}


@article{BR11,
  author    = {Thomas Bl{\"a}sius and
               Ignaz Rutter},
  title     = {Simultaneous {PQ}-Ordering with Applications to Constrained
               Embedding Problems},
  journal   = {CoRR},
  volume    = {abs/1112.0245},
  year      = {2011},
  ee        = {http://arxiv.org/abs/1112.0245},
    note = {\arxiv{1112.0245} (last accessed 9/21/2017)},
}

@incollection {HJL10,
   author = {Haeupler, Bernhard and Jampani, Krishnam and Lubiw, Anna},
   title = {Testing Simultaneous Planarity When the Common Graph Is 2-Connected},
   booktitle = {Algorithms and Computation},
   series = {Lecture Notes in Computer Science},
   editor = {Cheong, Otfried and Chwa, Kyung-Yong and Park, Kunsoo},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-17513-8},
   pages = {410-421},
   volume = {6507},
   year = {2010}
}

@article{HJL10a,
  author = {Haeupler, Bernhard and Jampani, Krishnam and Lubiw, Anna},
  title     = {Testing Simultaneous Planarity when the Common Graph is
               $2$-Connected},
  journal   = {CoRR},
  volume    = {abs/1009.4517},
  year      = {2010},
  ee        = {http://arxiv.org/abs/1009.4517},
    note = {\arxiv{1009.4517} (last accessed 9/21/2017)},
}

@Article{BEW95,
  author =	"Richard A. Becker and Stephen G. Eick and Allan R.
		 Wilks",
  title =	"Visualizing Network Data",
  journal =	"IEEE Transactions on Visualization and Computer
		 Graphics",
  volume =	"1",
  number =	"1",
  pages =	"16--28",
  month =	mar,
  year = 	"1995",
  ISSN = 	"1077-2626 (print), 1941-0506 (electronic), 2160-9306",
  issn-l =	"1077-2626",
  fjournal =	"IEEE Transactions on Visualization and Computer
		 Graphics",
}

@incollection {BK12,
   author = {Bruckdorfer, Till and Kaufmann, Michael},
   affiliation = {Wilhelm-Schickard-Institut f\"{u}r Informatik, Universit\"{a}t T\"{u}bingen, Germany},
   title = {Mad at Edge Crossings? {B}reak the Edges!},
   booktitle = {Fun with Algorithms},
   series = {Lecture Notes in Computer Science},
   editor = {Kranakis, Evangelos and Krizanc, Danny and Luccio, Flaminia},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-30346-3},
   keyword = {Computer Science},
   pages = {40-50},
   volume = {7288},
   year = {2012}
}

@article {AGKN12,
    AUTHOR = {Angelini, Patrizio and Geyer, Markus and Kaufmann, Michael and
              Neuwirth, Daniel},
     TITLE = {On a tree and a path with no geometric simultaneous embedding},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {16},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {37--83},
      ISSN = {1526-1719},
}

@article {H16,
    AUTHOR = {Hjelmslev, J.},
     TITLE = {Die {G}eometrie der {W}irklichkeit},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {40},
      YEAR = {1916},
    NUMBER = {1},
     PAGES = {35--66},
      ISSN = {0001-5962},
}

@article{H23,
   author = {Hjelmslev, J.},
   affiliation = {Kopenhagen},
   title = {Die nat\"{u}rliche {G}eometrie},
   journal = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t Hamburg},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0025-5858},
   keyword = {Mathematics and Statistics},
   pages = {1-36},
   volume = {2},
   issue = {1},
   year = {1923}
}

@book{W67,
  title={Wittgenstein und der Wiener Kreis: Gespr{\"{a}}che aufgezeichnet von Friedrich Waismann},
  author={Wittgenstein, Ludwig},
  volume={3},
  year={1967},
  publisher={Suhrkamp}
}

@article{WSP12,
author = "Andreas Wotzlaw and Ewald Speckenmeyer and Stefan Porschen",
title = "Generalized {$k$}-ary tanglegrams on level graphs: A satisfiability-based approach and its evaluation",
fjournal = "Discrete Applied Mathematics",
 journal = {Discrete Appl. Math.},
 issue_date = {November, 2012},
 volume = {160},
 number = {16-17},
 month = nov,
 year = {2012},
 issn = {0166-218X},
 pages = {2349--2363},
 numpages = {15},
 publisher = {Elsevier Science Publishers B. V.},
}

@article {FKP10,
    AUTHOR = {Fernau, Henning and Kaufmann, Michael and Poths, Mathias},
     TITLE = {Comparing trees via crossing minimization},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {76},
      YEAR = {2010},
    NUMBER = {7},
     PAGES = {593--608},
      ISSN = {0022-0000},
}

@article{FYX12,
author = "Kai Feng and Yaoyao Ye and Jiang Xu",
title = "A Formal Study on Topology and Floorplan Characteristics of Mesh and Torus-based Optical Networks-on-Chip",
journal = "Microprocessors and Microsystems",
year = "2012",
publisher = "Elsevier",
issn = "0141-9331",
doi = "10.1016/j.micpro.2012.06.010",
}

@inproceedings {F11,
    AUTHOR = {Feder, Elie},
     TITLE = {The maximum rectilinear crossing number of the wheel graph},
 BOOKTITLE = {Proceedings of the {F}orty-{S}econd {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory and {C}omputing},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {210},
      YEAR = {2011},
     PAGES = {21--32},
      ISSN = {0384-9864},
}

@misc{A13,
 author = {Aichholzer, Oswin},
 title = {On the Rectilinear Crossing Number},
 note = {Summary of results at \url{http://www.ist.tugraz.at/staff/aichholzer/research/rp/triangulations/crossing/} (last accessed 9/21/2017)},
}

%use AAFMRS13
@inproceedings{AAFMRS12,
  title = "{The $2$-page crossing number of {$K_n$}}",
  author = {{\'A}brego, Bernardo M. and Aichholzer, Oswin and Fern{\'a}ndez-Merchant, Silvia and
   Ramos, Pedro and Salazar, Gelasio},
  booktitle =	"Symposuim on Computational Geometry 2012, So{CG} '12,
		 Chapel Hill, {NC}, {USA}, June 17-20, 2012",
  publisher =	"ACM",
  year = 	"2012",
  editor =	"Tamal K. Dey and Sue Whitesides",
  ISBN = 	"978-1-4503-1299-8",
  pages =	"397--404",
}

@article {AAFMRS13,
    AUTHOR = {{\'A}brego, Bernardo M. and Aichholzer, Oswin and
              Fern{\'a}ndez-Merchant, Silvia and Ramos, Pedro and Salazar,
              Gelasio},
     TITLE = {The 2-{P}age {C}rossing {N}umber of {$K_n$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {49},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {747--777},
      ISSN = {0179-5376},
}

@inproceedings {AFI11,
    AUTHOR = {Alpert, Matthew and Feder, Elie and Isseroff, Yehuda},
     TITLE = {The maximum rectilinear crossing number of generalized wheel
              graphs},
 BOOKTITLE = {Proceedings of the {F}orty-{S}econd {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory and {C}omputing},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {209},
      YEAR = {2011},
     PAGES = {33--46},
      ISSN = {0384-9864},
}

@inproceedings {ABFH12,
    AUTHOR = {Alpert, Matthew and Bode, Jens-P. and Feder, Elie and
              Harborth, Heiko},
     TITLE = {The minimum of the maximum rectilinear crossing numbers of
              small cubic graphs},
 BOOKTITLE = {Proceedings of the {F}orty-{T}hird {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory and {C}omputing},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {214},
      YEAR = {2012},
     PAGES = {187--197},
      ISSN = {0384-9864},
}

@techreport{SG10,
  author =       "Stallmann, Matthias F. and Gupta, Saurabh",
  title =        "Bottleneck Crossing Minimization in Layered Graphs",
  institution = "North Carolina State University",
  year = "2010",
  number = "TR-2010-13",
  month="June",
}

@article{S12,
  author = {Stallmann, Matthias F.},
 title = {A heuristic for bottleneck crossing minimization and its performance on general crossing minimization: Hypothesis and experimental study},
 journal = {J. Exp. Algorithmics},
 fjournal = {Journal of Experimental Algorithmics},
 issue_date = {July 2012},
 volume = {17},
 number = {1},
 month = jul,
 year = {2012},
 issn = {1084-6654},
 pages = {1.3:1.1--1.3:1.30},
 publisher = {ACM},
 address = {New York, NY, USA},
}


%use dKPS13
@ARTICLE{dKPS12,
   author = {{de Klerk}, Etienne  and Pasechnik, Dmitrii V. and {Salazar}, Gelasio},
    title = "{Improved lower bounds on book crossing numbers of complete graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1207.5701},
    note = {\arxiv{1207.5701} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2012,
    month = jul,
   adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1207.5701D},
}

@article {dKPS13,
    AUTHOR = {de Klerk, E. and Pasechnik, D. V. and Salazar, G.},
     TITLE = {Improved lower bounds on book crossing numbers of complete
              graphs},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {27},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {619--633},
      ISSN = {0895-4801},
}

@article{MS11,
author = "Bojan Mohar and Tamon Stephen",
title = "Expected Crossing Numbers",
journal = "Electronic Notes in Discrete Mathematics",
volume = "38",
number = "0",
pages = "651--656",
year = "2011",
issn = "1571-0653",
}

@inproceedings{M08,
author = "Bojan Mohar",
title = "Crossing numbers of graphs on the plane and on other surfaces",
booktitle = "Abstracts of the 20th Workshop on Topological Graph Theory in Yokohama",
address = "Yokohama, Japan",
year = "2008",
}

@incollection {EK01,
   author = {Eiglsperger, Markus and Kaufmann, Michael},
   title = {An Approach for Mixed Upward Planarization},
   booktitle = {Algorithms and Data Structures},
   series = {Lecture Notes in Computer Science},
   editor = {Dehne, Frank and Sack, J\"{o}rg-R\"{u}diger and Tamassia, Roberto},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-540-42423-9},
   pages = {352-364},
   volume = {2125},
   year = {2001}
}

@incollection {KT12,
   author = {Kobayashi, Yasuaki and Tamaki, Hisao},
   affiliation = {Meiji University, Kawasaki, Japan 214-8571},
   title = {A Fast and Simple Subexponential Fixed Parameter Algorithm for One-Sided Crossing Minimization},
   booktitle = {Algorithms – ESA 2012},
   series = {Lecture Notes in Computer Science},
   editor = {Epstein, Leah and Ferragina, Paolo},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-33089-6},
   pages = {683-694},
   volume = {7501},
   year = {2012},
}

@article {DW04,
    AUTHOR = {Dujmovi{\'c}, Vida and Whitesides, Sue},
     TITLE = {An efficient fixed parameter tractable algorithm for 1-sided
              crossing minimization},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {40},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {15--31},
}

@misc{BVRK12,
  author="Bauer, Andreas and Vordermeier, Julian and Rutter, Ignaz and  Kaufmann, Michael",
  title="Cycle{X}ings",
  note = "Game presented at {\em Graph Drawing '12}",
  howpublished = {\url{http://i11www.iti.uni-karlsruhe.de/projects/cyclexings/index} (last accessed 1/9/2013)},
  year = "2012",
}

%use dKPS14
@ARTICLE{dKPS12b,
   author = {{de Klerk}, Etienne  and Pasechnik, Dmitrii V. and {Salazar}, Gelasio},
    title = "{Book drawings of complete bipartite graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1210.2918},
   note = {\arxiv{1210.2918} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2012,
    month = oct,

}

@article {dKPS14,
    AUTHOR = {de Klerk, Etienne and Pasechnik, Dmitrii V. and Salazar,
              Gelasio},
     TITLE = {Book drawings of complete bipartite graphs},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {167},
      YEAR = {2014},
     PAGES = {80--93},
      ISSN = {0166-218X},
   MRCLASS = {05C62},
  MRNUMBER = {3166108},
MRREVIEWER = {Grant Cairns},
       DOI = {10.1016/j.dam.2013.11.001},
       URL = {http://dx.doi.org/10.1016/j.dam.2013.11.001},
}

@article{Z12,
title = "(2)-pancyclic graphs",
journal = "Discrete Applied Mathematics",
volume = "161",
number = "7–8",
pages = "1128 - 1136",
year = "2013",
issn = "0166-218X",
doi = "10.1016/j.dam.2012.11.002",
author = "Carol T. Zamfirescu",
}

@mastersthesis{H12,
    author = "Hoske, Daniel",
    title = "Book Embedding with Fixed Page Assignments",
    advisor = "Bl{\"{a}}sius, Thomas and Rutter, Ignaz",
    school ="Karlsruhe Institute of Technology",
    year = "2012",
    address = "Karlsruhe, Germany",
    type = "Bachelor thesis",
}

@mastersthesis{G15,
    author = "Gei{\ss}er, Maximilian",
    title = "Kreuzungsminimierung bei simulatner Einbettung planarer Graphen",
    advisor = "Bl{\"{a}}sius, Thomas and Rutter, Ignaz",
    school ="Karlsruhe Institute of Technology",
    year = "2015",
    address = "Karlsruhe, Germany",
    type = "Bachelor thesis",
}

@misc{EKMSTWYY12,
 author = {Erickson, Lars and  Kim, John and McConvey, Andrew and Shar, Nathaniel and Tomlinson, Charles  and Wang, David
 and Yager, Derrek and Yeage, Elyse},
 title = {Linear Crossing Numbers of Graphs},
 note = {Results of a Combinatorics REGS program (\url{http://www.math.uiuc.edu/~west/regs/crossnum.html}, last accessed 9/21/2017))},
 year = {2012},
}

%no longer available online, use EKMSTWYY12
@misc{EKWY12,
 author = {Erickson, Lars and  Kim, John and Wang, David and Yeage, Elyse},
 title = {Airport Crossing Number},
 note = {Report of a Combinatorics REGS program},
 year = {2012},
}

@article{M88,
  title={On circular layouts},
  author={M{\"a}kinen, E.},
  journal={International Journal of Computer Mathematics},
  volume={24},
  number={1},
  pages={29--37},
  year={1988},
  publisher={Taylor \& Francis}
}

@book{EL92,
 author =	"Peter Eades and Wei Lai",
  title =	"Algorithms for Disjoint Node Images",
  pages =	"253--265",
  journal =	"Proc. 15th Australian Computer Science Conf.",
  volume =	"14",
  location =	"Hobart, Australia",
  month =	jan,
  publisher={Key Centre for Software Technology, Department of Computer Science, University of Queensland},
  year = 	"1992",
}

@techreport{ELMS91,
  title={Preserving the mental map of a diagram},
  author={Eades, Peter and Lai, Wei and Misue, Kazuo and Sugiyama, Kozo},
  month = {August},
  year={1991},
  publisher={International Institute for Advanced Study of Social Information Science},
  number = {IIAS-RR-91-16E},
  institution = {Fujitsu Limited},
  address = {Japan},
}

@article{STT81,
    AUTHOR = {Sugiyama, Kozo and Tagawa, Sh{\^o}jir{\^o} and Toda,
              Mitsuhiko},
     TITLE = {Methods for visual understanding of hierarchical system
              structures},
   JOURNAL = {IEEE Trans. Systems Man Cybernet.},
  FJOURNAL = {Institute of Electrical and Electronic Engineers. Transactions
              on Systems, Man, and Cybernetics},
    VOLUME = {11},
      YEAR = {1981},
    NUMBER = {2},
     PAGES = {109--125},
      ISSN = {0018-9472},
}

@incollection {BBBF09,
    AUTHOR = {Bachmaier, Christian and Brandenburg, Franz J. and Brunner,
              Wolfgang and F{\"u}l{\"o}p, Raymund},
     TITLE = {Coordinate assignment for cyclic level graphs},
 BOOKTITLE = {Computing and combinatorics},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {5609},
     PAGES = {66--75},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2009},
}

@article{MELS95,
  title={Layout adjustment and the mental map},
  author={Misue, K. and Eades, P. and Lai, W. and Sugiyama, K.},
  journal={Journal of visual languages and computing},
  volume={6},
  number={2},
  pages={183--210},
  year={1995},
  publisher={Elsevier}
}

@article {LE02,
    AUTHOR = {Lai, Wei and Eades, Peter},
     TITLE = {Removing edge-node intersections in drawings of graphs},
   JOURNAL = {Inform. Process. Lett.},
  FJOURNAL = {Information Processing Letters},
    VOLUME = {81},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {105--110},
      ISSN = {0020-0190},
}

@inproceedings{CMG13,
 author = {Chae, Sangwon and Majumder, Aditi and Gopi, M.},
 title = {{HD-GraphViz}: highly distributed graph visualization on tiled displays},
 booktitle = {Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing},
 series = {ICVGIP '12},
 year = {2012},
 isbn = {978-1-4503-1660-6},
 location = {Mumbai, India},
 pages = {43:1--43:8},
 articleno = {43},
 numpages = {8},
 url = {http://doi.acm.org/10.1145/2425333.2425376},
 publisher = {ACM},
 address = {New York, NY, USA},
}

%use M14
@ARTICLE{M13,
   author = {{Matou{\v{s}}ek}, Ji\v{r}\'{\i}},
    title = "{Near-optimal separators in string graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1302.6482},
   note = {\arxiv{1302.6482} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2013,
    month = feb,
}

@article {M14,
    AUTHOR = {Matou{\v{s}}ek, Ji{\v{r}}{\'{\i}}},
     TITLE = {Near-optimal separators in string graphs},
   JOURNAL = {Combin. Probab. Comput.},
  FJOURNAL = {Combinatorics, Probability and Computing},
    VOLUME = {23},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {135--139},
      ISSN = {0963-5483},
       DOI = {10.1017/S0963548313000400},
       URL = {http://dx.doi.org/10.1017/S0963548313000400},
}
	
%use AAPGCHLRNU16
@ARTICLE{AAPGCHLRNU13,
   author = {{Aichholzer}, O. and {Araujo-Pardo}, G. and {Garc{\'{\i}}a-Col{\'{\i}}n}, N. and
	{Hackl}, T. and {Lara}, D. and {Rubio-Montiel}, C. and {Urrutia}, J.
	},
    title = "{Geometric achromatic and pseudoachromatic indices}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1303.4673},
   note = {\arxiv{1303.4673} (last accessed 9/21/2017)},
     year = 2013,
    month = mar,
}

@article {AAPGCHLRNU16,
   author = {{Aichholzer}, O. and {Araujo-Pardo}, G. and {Garc{\'{\i}}a-Col{\'{\i}}n}, N. and
	{Hackl}, T. and {Lara}, D. and {Rubio-Montiel}, C. and {Urrutia}, J.
	},
     TITLE = {Geometric achromatic and pseudoachromatic indices},
   JOURNAL = {Graphs Combin.},
  FJOURNAL = {Graphs and Combinatorics},
    VOLUME = {32},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {431--451},
      ISSN = {0911-0119},
   MRCLASS = {05C10 (05C15 05C62)},
  MRNUMBER = {3461960},
MRREVIEWER = {Luciano Norberto Grippo},
       DOI = {10.1007/s00373-015-1610-x},
       URL = {http://dx.doi.org/10.1007/s00373-015-1610-x},
}

@misc{E13,
 author = "David Eppstein",
 title = "An early reference on crossing minimization",
 howpublished = {\url{https://11011110.github.io/blog/2013/03/27/early-reference-on.html} (last accessed 9/21/2017)},
}

@misc{E13a,
 author = "David Eppstein",
 title = "A Brief History of Curves in Graph Drawing",
 howpublished = {\url{https://11011110.github.io/blog/2013/04/08/brief-history-of.html} (last accessed 9/21/2017)},
}

@misc{E13b,
 author = "David Eppstein",
 title = "Big batch of graph drawing preprints",
 howpublished = {\url{http://11011110.livejournal.com/275238.html} (last accessed 2013/9/4)},
}

@book{B45,
  title={The measurement of sociometric status, structure and development},
  author={Bronfenbrenner, Urie},
  series = {Sociometry monographs},
  number={6},
  year={1945},
  pages = {80},
  publisher={New York: Beacon House}
}

@book{M34,
  title={Who shall survive?: A new approach to the problem of human interrelations.},
  author={Moreno, Jacob Levy},
  year={1934},
  publisher={Nervous and Mental Disease Publishing Co},
  address = {Washington, D.C.},
  pages = {xvi+437},
}

@book{M53,
  title={Who shall survive?: A new approach to the problem of human interrelations.},
  author={Moreno, Jacob Levy},
  year={1934},
  publisher={Beacon House Inc},
  address = {Beacon, N.Y.},
  pages = {cxiv+718},
}

@article{N40,
     title = {A Method for Depicting Social Relationships Obtained by Sociometric Testing},
     author = {Northway, Mary L.},
     journal = {Sociometry},
     volume = {3},
     number = {2},
     month = apr,
     pages = {pp. 144-150},
     url = {http://www.jstor.org/stable/2785439},
     ISSN = {00380431},
     language = {English},
     year = {1940},
     publisher = {American Sociological Association},
}

 @incollection {M99a,
    AUTHOR = {Mohar, Bojan},
     TITLE = {Drawing graphs in the hyperbolic plane},
     crossref = {K99},
     PAGES = {127--136},
}

@proceedings {K99,
     TITLE = {Graph drawing},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {1731},
 BOOKTITLE = {Proceedings of the 7th {I}nternational {S}ymposium ({GD}'99)
              held at \v {S}ti\v r\'\i n {C}astle, {S}eptember 15--19, 1999},
    EDITOR = {Kratochv{\'{\i}}l, Jan},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1999},
     PAGES = {xiv+422},
      ISBN = {3-540-66904-3},
}

@article{B51,
  title={A diagnostic note on the construction of sociograms and action diagrams},
  author={Borgatta, Edgar F.},
  journal={Group Psychotherapy},
  volume={3},
  pages={300--308},
  year={1951},
}

@incollection {C11,
    AUTHOR = {Chuzhoy, Julia},
     TITLE = {An algorithm for the graph crossing number problem [extended
              abstract]},
 BOOKTITLE = {S{TOC}'11---{P}roceedings of the 43rd {ACM} {S}ymposium on
              {T}heory of {C}omputing},
     PAGES = {303--312},
 PUBLISHER = {ACM},
   ADDRESS = {New York},
      YEAR = {2011},
}

%use CS18
@ARTICLE{CS13,
   author = {{Chekuri}, Chandra and {Sidiropoulos}, Anastasios},
    title = "{Approximation algorithms for Euler genus and related problems}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1304.2416},
      note = {\arxiv{1304.2416} (last accessed 9/21/2017)},
     year = 2013,
    month = apr,
}

@article {CS18,
    AUTHOR = {Chekuri, Chandra and Sidiropoulos, Anastasios},
     TITLE = {Approximation algorithms for {E}uler genus and related
              problems},
   JOURNAL = {SIAM J. Comput.},
  FJOURNAL = {SIAM Journal on Computing},
    VOLUME = {47},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {1610--1643},
      ISSN = {0097-5397},
   MRCLASS = {68W25 (05C10 68R10 68W40)},
  MRNUMBER = {3842928},
       DOI = {10.1137/14099228X},
       URL = {https://doi.org/10.1137/14099228X},
}

@incollection {CS13b,
    AUTHOR = {Chekuri, Chandra and Sidiropoulos, Anastasios},
     TITLE = {Approximation algorithms for {E}uler genus and related
              problems},
 BOOKTITLE = {2013 {IEEE} 54th {A}nnual {S}ymposium on {F}oundations of
              {C}omputer {S}cience---{FOCS} 2013},
     PAGES = {167--176},
 PUBLISHER = {IEEE Computer Soc., Los Alamitos, CA},
      YEAR = {2013},
   MRCLASS = {05C85 (05C10 68W25)},
  MRNUMBER = {3246218},
       DOI = {10.1109/FOCS.2013.26},
       URL = {http://dx.doi.org/10.1109/FOCS.2013.26},
}


%use BCE13b
@ARTICLE{BCE13,
   author = {{Bannister}, Michael~J. and {Cabello}, Sergio and {Eppstein}, David},
    title = "{Parameterized Complexity of 1-Planarity}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1304.5591},
      note = {\arxiv{1304.5591} (last accessed 9/21/2017)},
     year = 2013,
    month = apr,
}

@incollection {BCE13b,
    AUTHOR = {Bannister, Michael J. and Cabello, Sergio and Eppstein, David},
     TITLE = {Parameterized complexity of 1-planarity},
 BOOKTITLE = {Algorithms and data structures},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8037},
     PAGES = {97--108},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2013},
   MRCLASS = {68Q25},
  MRNUMBER = {3126349},
       DOI = {10.1007/978-3-642-40104-6_9},
       URL = {http://dx.doi.org/10.1007/978-3-642-40104-6_9},
}

%use CM13
@ARTICLE{CM12,
   author = {{Cabello}, Sergio and {Mohar}, Bojan},
    title = "{Adding one edge to planar graphs makes crossing number and 1-planarity hard}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1203.5944},
      note = {\arxiv{1203.5944} (last accessed 9/21/2017)},
     year = 2012,
    month = mar,
}

@article{CM13,
author = {{Cabello}, Sergio and {Mohar}, Bojan},
title = {Adding One Edge to Planar Graphs Makes Crossing Number and $1$-Planarity Hard},
journal = {SIAM Journal on Computing},
volume = {42},
number = {5},
pages = {1803-1829},
year = {2013},
doi = {10.1137/120872310},

URL = {http://epubs.siam.org/doi/abs/10.1137/120872310},
eprint = {http://epubs.siam.org/doi/pdf/10.1137/120872310}
}

%use FPW15
@ARTICLE{FP13,
   author = {{Fink}, Martin and {Pupyrev}, Sergey},
    title = "{Ordering Metro Lines by Block Crossings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1305.0069},
      note = {\arxiv{1305.0069} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
     year = 2013,
    month = apr,
}

@article {FPW15,
    AUTHOR = {Fink, Martin and Pupyrev, Sergey and Wolff, Alexander},
     TITLE = {Ordering metro lines by block crossings},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {19},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {111--153},
      ISSN = {1526-1719},
   MRCLASS = {05C85},
  MRNUMBER = {3321741},
       DOI = {10.7155/jgaa.00351},
       URL = {http://dx.doi.org/10.7155/jgaa.00351},
}


%use FP13b

@ARTICLE{FP13a,
   author = {{Fink}, Martin and {Pupyrev}, Sergey},
    title = "{Metro-Line Crossing Minimization: Hardness, Approximations, and Tractable Cases}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1306.2079},
         note = {\arxiv{1306.2079} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
     year = 2013,
    month = jun,
}

@incollection {FP13b,
    AUTHOR = {Fink, Martin and Pupyrev, Sergey},
     TITLE = {Metro-line crossing minimization: hardness, approximations,
              and tractable cases},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8242},
     PAGES = {328--339},
 PUBLISHER = {Springer, Cham},
      YEAR = {2013},
   MRCLASS = {68R10 (05C62 68Q25)},
  MRNUMBER = {3162034},
       DOI = {10.1007/978-3-319-03841-4_29},
       URL = {http://dx.doi.org/10.1007/978-3-319-03841-4_29},
}

@article {FM07,
    AUTHOR = {Fabrici, Igor and Madaras, Tom{\'a}{\v{s}}},
     TITLE = {The structure of 1-planar graphs},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {307},
      YEAR = {2007},
    NUMBER = {7-8},
     PAGES = {854--865},
      ISSN = {0012-365X},
}

@article{CH13,
  title={On drawings and decompositions of 1-planar graphs},
  author={Czap, J{\'u}lius and Hud{\'a}k, D{\'a}vid},
  journal={The Electronic Journal of Combinatorics},
  volume={20},
  number={2},
  pages={P54},
  year={2013}
}

@incollection{KMNT13,
author={Kobayashi, Yasuaki and Maruta, Hirokazu and Nakae, Yusuke and Tamaki, Hisao},
title={A Linear Edge Kernel for Two-Layer Crossing Minimization},
year={2013},
isbn={978-3-642-38767-8},
booktitle={Computing and Combinatorics},
volume={7936},
series={Lecture Notes in Computer Science},
editor={Du, Ding-Zhu and Zhang, Guochuan},
publisher={Springer Berlin Heidelberg},
pages={458-468},
}

@incollection {CK03,
    AUTHOR = {Chen, Zhi-Zhong and Kouno, Mitsuharu},
     TITLE = {A linear-time algorithm for $7$-coloring $1$-planar graphs
              (extended abstract)},
 BOOKTITLE = {Mathematical foundations of computer science 2003},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2747},
     PAGES = {348--357},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
}

@article {E86,
    AUTHOR = {Eggleton, Roger B.},
     TITLE = {Rectilinear drawings of graphs},
   JOURNAL = {Utilitas Math.},
  FJOURNAL = {Utilitas Mathematica. An International Journal of Discrete and
              Combinatorial Mathematics, and Statistical Design},
    VOLUME = {29},
      YEAR = {1986},
     PAGES = {149--172},
      ISSN = {0315-3681},
}

@ARTICLE{OTU13,
   author = {{Okamoto}, Yoshio and {Tatsu}, Yuichi and {Uno}, Yushi},
    title = "{Exact and fixed-parameter algorithms for metro-line crossing minimization problems}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1306.3538},
    note = {\arxiv{1306.3538} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
     year = 2013,
    month = jun,
}

@book {H74,
    AUTHOR = {Hotz, G{\"u}nter},
     TITLE = {Schaltkreistheorie},
 PUBLISHER = {Walter de Gruyter, Berlin-New York},
      YEAR = {1974},
     PAGES = {336},
}

@phdthesis {B70,
    AUTHOR = {Barton, Calvin Pascal},
     TITLE = {The Rectilinear Crossing Number for Complete
              Simple Graphs in $E_2$},
      school = {The University of Texas at Austin},
      address = {Austin, Texas},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1970},
     PAGES = {45},
}

@inproceedings {G68,
    AUTHOR = {Guy, Richard K.},
    TITLE = {The planar and toroidal crossing numbers of {$K_{n}$}},
    Booktitle = {Beitr\"{a}ge zur {G}raphentheorie},
    editor = {Sachs, Hans and Vo\ss, Heinz-J\"{u}rgen and Walther, Hansjoachim},
    YEAR = {1968},
    publisher = {B.G. Teubner},
    address = {Leipzig},
    PAGES = {37--39},
}

@unpublished{FDPK13?,
 author = {Filippova, Darya  and Duggal, Geet  and Patro, Rob and Kingsford, Carl},
 title = {ChromoVis: Feature-Rich Layouts of Chromosome Conformation Graphs},
 note = {Unpublished manuscript at \url{http://www.cs.cmu.edu/~dfilippo/projects/chromovis/chromovisGD2013.pdf} (last accessed 9/21/2017)},
 year = 2013,
}


@article {CRS13,
    AUTHOR = {Christian, Robin and Richter, R. Bruce and Salazar, Gelasio},
     TITLE = {Zarankiewicz's conjecture is finite for each fixed {$m$}},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {103},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {237--247},
      ISSN = {0095-8956},
}



@incollection {BK64,
    AUTHOR = {Bla{\v{z}}ek, Jaroslav and Koman, Milan},
     TITLE = {A minimal problem concerning complete plane graphs},
 BOOKTITLE = {Theory of {G}raphs and its {A}pplications ({P}roc. {S}ympos.
              {S}molenice, 1963)},
     PAGES = {113--117},
 PUBLISHER = {Publ. House Czechoslovak Acad. Sci., Prague},
      YEAR = {1964},
}

@article {BK67,
    AUTHOR = {Bla{\v{z}}ek, Jaroslav and Koman, Milan},
     TITLE = {On an extremal problem concerning graphs},
   JOURNAL = {Comment. Math. Univ. Carolinae},
  FJOURNAL = {Commentationes Mathematicae Universitatis Carolinae},
    VOLUME = {8},
      YEAR = {1967},
     PAGES = {49--52},
      ISSN = {0010-2628},
}

@article {DGK11,
    AUTHOR = {Duncan, Christian A. and Goodrich, Michael T. and Kobourov,
              Stephen G.},
     TITLE = {Planar drawings of higher-genus graphs},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {15},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {7--32},
      ISSN = {1526-1719},
}

@InProceedings{LPVV01,
  author =	"Lazarus, Francis  and Pocchiola, Michel  and Vegter, Gert
		 and Verroust, Anne ",
  title =	"Computing a canonical polygonal schema of an orientable triangulated surface",
  pages =	"80--89",
  booktitle =	"Proceedings of the Seventeenth Annual Symposium on
		 Computational Geometry ({SCG}-01)",
  month =	jun # " ~3--5",
  publisher =	"ACM Press",
  address =	"New York",
  year = 	"2001",
}

@article {EHP04,
    AUTHOR = {Erickson, Jeff and Har-Peled, Sariel},
     TITLE = {Optimally cutting a surface into a disk},
      NOTE = {ACM Symposium on Computational Geometry (Barcelona, 2002)},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {31},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {37--59},
      ISSN = {0179-5376},
}

@article {DS95,
    AUTHOR = {Dey, T. K. and Schipper, H.},
     TITLE = {A new technique to compute polygonal schema for
              {$2$}-manifolds with application to null-homotopy detection},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {14},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {93--110},
      ISSN = {0179-5376},
}

@mastersthesis{L13,
 author = {L\'{o}pez, Lorena Mercedes },
 title = {Rectilinear crossing numbers of complete graphs with specific nested sequence of convex hulls},
    advisor = "\'{A}brego, Bernardo M. and Fern\'{a}ndez, Silvia ",
    school ="California State University",
    year = "2013",
    address = "Northridge",
}

@article {W77,
    AUTHOR = {Warfield, John N.},
     TITLE = {Crossing theory and hierarchy mapping},
   JOURNAL = {IEEE Trans. Systems Man Cybernet.},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Systems, Man, and Cybernetics},
    VOLUME = {SMC-7},
      YEAR = {1977},
    NUMBER = {7},
     PAGES = {505--523},
      ISSN = {0018-9472},
}

%use BES13b
@ARTICLE{BES13,
   author = {{Bannister}, Michael~J. and {Eppstein}, David and {Simons}, Joseph~A.},
    title = "{Fixed parameter tractability of crossing minimization of almost-trees}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1308.5741},
    note = {\arxiv{1308.5741} (last accessed 9/21/2017)},
 primaryClass = "cs.CG",
 keywords = {Computer Science - Computational Geometry},
     year = 2013,
    month = aug,
}

@incollection {BES13b,
    AUTHOR = {Bannister, Michael J. and Eppstein, David and Simons, Joseph
              A.},
     TITLE = {Fixed parameter tractability of crossing minimization of
              almost-trees},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8242},
     PAGES = {340--351},
 PUBLISHER = {Springer, Cham},
      YEAR = {2013},
   MRCLASS = {68R10 (05C62 68Q25)},
  MRNUMBER = {3162035},
       DOI = {10.1007/978-3-319-03841-4_30},
       URL = {http://dx.doi.org/10.1007/978-3-319-03841-4_30},
}

%use BE14b
@ARTICLE{BE14,
   author = {Bannister, Michael~J. and Eppstein, David},
    title = "{Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1408.6321},
    note = {\arxiv{1408.6321} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",  year = 2014,
    month = aug,
}

@incollection {BE14b,
    AUTHOR = {Bannister, Michael J. and Eppstein, David},
     TITLE = {Crossing minimization for 1-page and 2-page drawings of graphs
              with bounded treewidth},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8871},
     PAGES = {210--221},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2014},
   MRCLASS = {05C62 (68R10)},
  MRNUMBER = {3333228},
       DOI = {10.1007/978-3-662-45803-7_18},
       URL = {http://dx.doi.org/10.1007/978-3-662-45803-7_18},
}



@Article{S13a,
   author = {Schaefer, Marcus},
   title = {Toward a Theory of Planarity: {H}anani-{T}utte and Planarity Variants},
   journal = {Journal of Graph Algortihms and Applications},
   year = {2013},
   volume = {17},
   number = {4},
   pages = {367--440},
}

@book {dL13,
    AUTHOR = {de Longueville, Mark},
     TITLE = {A course in topological combinatorics},
    SERIES = {Universitext},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2013},
     PAGES = {xii+238},
      ISBN = {978-1-4419-7909-4; 978-1-4419-7910-0},
       DOI = {10.1007/978-1-4419-7910-0},
       URL = {http://dx.doi.org/10.1007/978-1-4419-7910-0},
}



@incollection {ABBGHNR13,
    AUTHOR = {Auer, Christopher and Bachmaier, Christian  and  Brandenburg, Franz J. and
    Glei{\ss}ner, Andreas and Hanauer, Kathrin and Neuwirth, Daniel and Reislhuber, Josef },
     TITLE = {Recognizing Outer $1$-Planar Graphs in Linear Time},
     pages = {108--119},
    crossref = {WW13},
}

% use ABDLDGMPT13a
@ARTICLE{ABDLDGMPT13,
   author = {Angelini, Patrizio and Binucci, Carla and Da Lozzo, Giordano and Didimo, Walter and
    Grilli, Luca and Montecchiani, Fabrizio and Patrignani, Maurizio and Tollis, Ioannis G.},
    title = "Drawings of Non-planar Graphs with Crossing-free Subgraphs",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1308.6706},
    note = {\arxiv{1308.6706} (last accessed 9/21/2017)},
 primaryClass = "cs.CG",
 keywords = {Computer Science - Computational Geometry},
     year = 2013,
    month = aug,
}

@inproceedings{ABDLDGMPT13a,
   author = {Angelini, Patrizio and Binucci, Carla and Da Lozzo, Giordano and Didimo, Walter and
    Grilli, Luca and Montecchiani, Fabrizio and Patrignani, Maurizio and Tollis, Ioannis G.},
    title = "Drawings of Non-planar Graphs with Crossing-free Subgraphs",
    pages = {295--306},
    crossref = {WW13},
}


@proceedings {WW13,
     TITLE = {Graph drawing},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {8242},
 BOOKTITLE = {Proceedings of the 21st {I}nternational {S}ymposium ({GD}'13)
              {S}eptember 23--25, 2013},
    EDITOR = {Wismath, Stephen  and Wolff, Alexander },
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2013},
     PAGES = {xiv+539},
}

@unpublished{SS09,
    AUTHOR = {Schaefer, Marcus and {\v{S}}tefankovi{\v{c}}, Daniel},
     TITLE = {Fixed Points, {N}ash Equilibria, and the Existential Theory of the Reals},
      NOTE = {Unpublished manuscript.},
      year = {2009},
}

@misc{W12,
   author = "Wikipedia",
   title = "Existential theory of the reals",
   year = "2012",
   note = "\url{http://en.wikipedia.org/wiki/Existential_theory_of_the_reals} (Online; accessed 17-July-2013)",
 }

 @techreport{N13,
  title={Straight-line Drawability of Embedded Graphs},
  author={Nagamochi, Hiroshi},
  year = "2013",
  number = "Technical Report 2013-005",
  institution = "Kyoto University",
  url = "\url{http://www.amp.i.kyoto-u.ac.jp/tecrep/index-e.html}",
}

@InProceedings{HELP12,
  title =	"{F}{\'a}ry's Theorem for 1-Planar Graphs",
  author =	"Seok-Hee Hong and Peter Eades and Giuseppe Liotta and
		 Sheung-Hung Poon",
  booktitle =	"Computing and Combinatorics - 18th Annual
		 International Conference, {COCOON} 2012",
  publisher =	"Springer",
  year = 	"2012",
  volume =	"7434",
  editor =	"Joachim Gudmundsson and Juli{\'a}n Mestre and Taso
		 Viglas",
  ISBN = 	"978-3-642-32240-2",
  pages =	"335--346",
  series =	"Lecture Notes in Computer Science",
}

@article {JKR13,
    AUTHOR = {Jel{\'{\i}}nek, V{\'{\i}}t and Kratochv{\'{\i}}l, Jan and
              Rutter, Ignaz},
     TITLE = {A {K}uratowski-type theorem for planarity of partially
              embedded graphs},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {46},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {466--492},
      ISSN = {0925-7721},
}

%use AS15
@ARTICLE{AS13,
   author = {{Anshu}, Anurag and {Shannigrahi}, Saswata},
    title = "{A Lower Bound on the Crossing Number of Uniform Hypergraphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1309.3625},
    note = {\arxiv{1309.3625} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics},
     year = 2013,
    month = sep,
}

@article{AS15,
author = "Anurag Anshu and Saswata Shannigrahi",
title = "A lower bound on the crossing number of uniform hypergraphs ",
journal = "Discrete Applied Mathematics ",
volume = "",
number = "",
pages = " - ",
year = "2015",
note = "",
issn = "0166-218X",
doi = "http://dx.doi.org/10.1016/j.dam.2015.10.009",
url = "http://www.sciencedirect.com/science/article/pii/S0166218X15004965",

}

%use AGSV17
@ARTICLE{AGSV15,
   author = {{Anshu}, Anurag and {Gangopadhyay}, Rahul and {Shannigrahi}, Saswata and
	{Vusirikala}, Satyanarayana},
    title = "{On the Rectilinear Crossing Number of Complete Uniform Hypergraphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1512.01335},
    note = {\arxiv{1512.01335} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics},
     year = 2015,
    month = dec,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv151201335A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {AGSV17,
    AUTHOR = {Anshu, Anurag and Gangopadhyay, Rahul and Shannigrahi, Saswata
              and Vusirikala, Satyanarayana},
     TITLE = {On the rectilinear crossing number of complete uniform
              hypergraphs},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {61},
      YEAR = {2017},
     PAGES = {38--47},
      ISSN = {0925-7721},
   MRCLASS = {52B55 (05C62 05C85 52B70 68U05)},
  MRNUMBER = {3582386},
MRREVIEWER = {Andrew Vince},
       DOI = {10.1016/j.comgeo.2016.11.001},
       URL = {http://dx.doi.org/10.1016/j.comgeo.2016.11.001},
}
	

%use AAFMRS14
@ARTICLE{AAFMRS13a,
   author = {{{\'A}brego}, Bernardo~M. and {Aichholzer}, Oswin and {Fern{\'a}ndez-Merchant}, Silvia and
	{Ramos}, Pedro and {Salazar}, Gelasio},
    title = "{Shellable drawings and the cylindrical crossing number of $K_n$}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1309.3665},
    note = {\arxiv{1309.3665} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Computational Geometry, 05C10, 05C62, 52C10},
     year = 2013,
    month = sep,
}

@article {AAFMRS14,
   author = {{{\'A}brego}, Bernardo~M. and {Aichholzer}, Oswin and {Fern{\'a}ndez-Merchant}, Silvia and
	{Ramos}, Pedro and {Salazar}, Gelasio},
     TITLE = {Shellable drawings and the cylindrical crossing number of
              {$K_n$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {52},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {743--753},
      ISSN = {0179-5376},
   MRCLASS = {05C62 (05C10 57M15)},
  MRNUMBER = {3279547},
MRREVIEWER = {Mari\'an Kle\v s\v c},
       DOI = {10.1007/s00454-014-9635-0},
       URL = {http://dx.doi.org/10.1007/s00454-014-9635-0},
}

@ARTICLE{ADFMLS16,
   author = {{{\'A}brego}, Bernardo~M. and {Dandurand}, Julia and {Fern{\'a}ndez-Merchant}, Silvia and
	{Lagoda}, Evgeniya and {Sapozhnikov}, Yakov},
    title = "{Book crossing numbers of the complete graph and small local convex crossing numbers}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1607.00131},
    note = {\arxiv{1607.00131} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 05C62, 52C10, 68R10},
     year = 2016,
    month = jul,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160700131A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{AAFMRS13b,
   author = {{{\'A}brego}, Bernardo~M. and {Aichholzer}, Oswin and {Fern{\'a}ndez-Merchant}, Silvia and
	{Ramos}, Pedro and {Salazar}, Gelasio},
title = "More on the crossing number of ${K}_n$: Monotone drawings ",
journal = "Electronic Notes in Discrete Mathematics ",
volume = "44",
number = "0",
pages = "411--414",
year = "2013",
note = "",
issn = "1571-0653",
doi = "http://dx.doi.org/10.1016/j.endm.2013.10.064",
url = "http://www.sciencedirect.com/science/article/pii/S1571065313002801",
}

@article{S13b,
  title={The Graph Crossing Number and its Variants: A Survey},
  author={Schaefer, Marcus},
  journal={The Electronic Journal of Combinatorics},
  volume={20},
  issue = {2},
  pages={1--90},
  year={2013},
  note = {Dynamic Survey, \#DS21},
}

@inproceedings{C88,
 author = {John Canny},
 title = {Some algebraic and geometric computations in PSPACE},
 booktitle = {STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing},
 year = {1988},
 isbn = {0-89791-264-0},
 pages = {460--469},
 location = {Chicago, Illinois, United States},
 doi = {http://doi.acm.org/10.1145/62212.62257},
 publisher = {ACM},
 address = {New York, NY, USA},
 }


@ARTICLE{GKT13,
   author = {{Grigoriev}, Alexander and {Koutsonas}, Athanassios and {Thilikos}, Dimitrios~M.},
    title = "{Nearly Planar Graphs and $\lambda$-flat Graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1311.0137},
    note = {\arxiv{1311.0137} (last accessed 9/21/2017)},
     year = 2013,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1311.0137G},
}

@incollection{FdFRV13,
year={2013},
isbn={978-3-642-45042-6},
booktitle={Graph-Theoretic Concepts in Computer Science},
volume={8165},
series={Lecture Notes in Computer Science},
editor={Brandstädt, Andreas and Jansen, Klaus and Reischuk, Rüdiger},
doi={10.1007/978-3-642-45043-3_22},
title={The Same Upper Bound for Both: The 2-Page and the Rectilinear Crossing Numbers of the n-Cube},
url={http://dx.doi.org/10.1007/978-3-642-45043-3_22},
publisher={Springer Berlin Heidelberg},
keywords={two-page crossing number; rectilinear crossing number; n-cube; topological graph theory},
author={Faria, Luerbio and Figueiredo, Celina M. H. and Richter, R. Bruce and V{\v{r}}{\v{t}}o, Imrich},
pages={249-260}
}

@article {M91,
author = {Madej, Tom},
title = {Bounds for the crossing number of the ${N}$-cube},
journal = {Journal of Graph Theory},
volume = {15},
number = {1},
publisher = {Wiley},
issn = {1097-0118},
url = {http://dx.doi.org/10.1002/jgt.3190150109},
doi = {10.1002/jgt.3190150109},
pages = {81--97},
year = {1991},
}

%use S14d
@ARTICLE{S13,
   author = {{Schaefer}, Marcus},
    title = "{Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1311.6839},
    note = {\arxiv{1311.6839} (last accessed 9/21/2017)},
 primaryClass = "cs.CG",
 keywords = {Computer Science - Computational Geometry, Computer Science - Computational Complexity, Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 68R10},
     year = 2013,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1311.6839S},
}

@incollection {S14d,
    AUTHOR = {Schaefer, Marcus},
     TITLE = {Picking planar edges; or, drawing a graph with a planar
              subgraph},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8871},
     PAGES = {13--24},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2014},
   MRCLASS = {05C62 (05C10 68R10 68U05)},
  MRNUMBER = {3333212},
       DOI = {10.1007/978-3-662-45803-7_2},
       URL = {http://dx.doi.org/10.1007/978-3-662-45803-7_2},
}


@incollection{CZ13,
year={2013},
isbn={978-3-642-36762-5},
booktitle={Graph Drawing},
volume={7704},
series={Lecture Notes in Computer Science},
editor={Didimo, Walter and Patrignani, Maurizio},
doi={10.1007/978-3-642-36763-2_22},
title={Upward Planarity Testing via {SAT}},
url={http://dx.doi.org/10.1007/978-3-642-36763-2_22},
publisher={Springer Berlin Heidelberg},
author={Chimani, Markus and Zeranski, Robert},
pages={248-259}
}

%use Z14
@ARTICLE{Z13,
   author = {{Zhang}, Xin},
    title = "{Drawing complete multipartite graphs on the plane with restrictions on crossings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1311.1994},
    note = {\arxiv{1311.1994} (last accessed 9/21/2017)},
     year = 2013,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1311.1994Z},
}

@article {Z14,
    AUTHOR = {Zhang, Xin},
     TITLE = {Drawing complete multipartite graphs on the plane with
              restrictions on crossings},
   JOURNAL = {Acta Math. Sin. (Engl. Ser.)},
  FJOURNAL = {Acta Mathematica Sinica (English Series)},
    VOLUME = {30},
      YEAR = {2014},
    NUMBER = {12},
     PAGES = {2045--2053},
      ISSN = {1439-8516},
   MRCLASS = {05C10 (05C62 68R10)},
  MRNUMBER = {3285933},
MRREVIEWER = {Robert Cimikowski},
       DOI = {10.1007/s10114-014-3763-6},
       URL = {https://doi.org/10.1007/s10114-014-3763-6},
}


@inproceedings{CZ14,
author= {Chimani, Markus and Zeranski, Robert},
title={An Exact Approach To Upward Crossing Minimization},
booktitle = {SIAM Meeting on Algorithm Engineering \& Experiments (ALENEX'14)},
year = {2014},

}

@article{D13,
 author = {Didimo, Walter},
 title = {Density of Straight-line 1-planar Graph Drawings},
 journal = {Inf. Process. Lett.},
 volume = {113},
 number = {7},
 month = apr,
 year = {2013},
 issn = {0020-0190},
 pages = {236--240},
 numpages = {5},
 url = {http://dx.doi.org/10.1016/j.ipl.2013.01.013},
 doi = {10.1016/j.ipl.2013.01.013},
 publisher = {Elsevier North-Holland, Inc.},
 address = {Amsterdam, The Netherlands, The Netherlands},
}


@article{SSS13,
author={Satsangi, Dharna and Srivastava, Kamal and Srivastava, Gursaran},
title={${K}$-page crossing number minimization problem: An evaluation of heuristics and its solution using {GESAKP}},
year={2013},
issn={1865-9284},
journal={Memetic Computing},
volume={5},
number={4},
doi={10.1007/s12293-013-0115-5},
url={http://dx.doi.org/10.1007/s12293-013-0115-5},
publisher={Springer Berlin Heidelberg},
pages={255-274},
language={English}
}

%use BFK15
@ARTICLE{BFK13,
   author = {{Balko}, Martin and {Fulek}, Radoslav and {Kyn{\v c}l}, Jan},
    title = "{Crossing numbers and combinatorial characterization of monotone drawings of ${K}_n$}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1312.3679},
    note = {\arxiv{1312.3679} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10},
     year = 2013,
    month = dec,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1312.3679B},
}

@article {BFK15,
    AUTHOR = {Balko, Martin and Fulek, Radoslav and {Kyn{\v c}l}, Jan},
     TITLE = {Crossing numbers and combinatorial characterization of
              monotone drawings of {$K_n$}},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {53},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {107--143},
      ISSN = {0179-5376},
   MRCLASS = {05C10},
  MRNUMBER = {3293491},
       DOI = {10.1007/s00454-014-9644-z},
       URL = {http://dx.doi.org/10.1007/s00454-014-9644-z},
}

@article{SSvH13,
author = "Schulze, Christoph Daniel and Sp{\"o}nemann, Miro  and von Hanxleden, Reinhard",
title = "Drawing layered graphs with port constraints ",
journal = "Journal of Visual Languages \& Computing ",
volume = "",
number = "",
pages = "",
year = "2013",
note = "",
issn = "1045-926X",
doi = "http://dx.doi.org/10.1016/j.jvlc.2013.11.005",
url = "http://www.sciencedirect.com/science/article/pii/S1045926X13000943",
}

@article{DV13,
author="Dobre, Cristian and Vera, Juan",
title = "Exploiting Symmetry in Copositive Programs via Semidefinite Hierarchies",
journal="Optimization Online",
howpublished = "\url(http://www.optimization-online.org/DB_HTML/2013/12/4181.html)",
year = 2013,
}

@article {A08,
    AUTHOR = {Albertson, Michael O.},
     TITLE = {Chromatic number, independence ratio, and crossing number},
   JOURNAL = {Ars Math. Contemp.},
  FJOURNAL = {Ars Mathematica Contemporanea},
    VOLUME = {1},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--6},
      ISSN = {1855-3966},
}
		
@article{PS14,
	author = {Poon, Patrick and Stout, Quentin},
	title = {An Optimal Time-Power Tradeoff for Sorting on a Mesh-Connected Computer with On-Chip Optics},
	journal = {International Journal of Networking and Computing},
	volume = {4},
	number = {1},
	year = {2014},
    pages = {70--87},
	issn = {2185-2847},	url = {http://ijnc.org/index.php/ijnc/article/view/74}
}

@article {PPST05,
    AUTHOR = {Pach, J{\'a}nos and Pinchasi, Rom and Sharir, Micha and
              T{\'o}th, G{\'e}za},
     TITLE = {Topological graphs with no large grids},
   JOURNAL = {Graphs Combin.},
  FJOURNAL = {Graphs and Combinatorics},
    VOLUME = {21},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {355--364},
      ISSN = {0911-0119},
}

@article {TT07,
    AUTHOR = {Tardos, G{\'a}bor and T{\'o}th, G{\'e}za},
     TITLE = {Crossing stars in topological graphs},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {21},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {737--749},
      ISSN = {0895-4801},
}

@article {FPS13,
    AUTHOR = {Fox, Jacob and Pach, J{\'a}nos and Suk, Andrew},
     TITLE = {The number of edges in {$k$}-quasi-planar graphs},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {27},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {550--561},
      ISSN = {0895-4801},
}

@article {SV93,
    AUTHOR = {S{\'y}kora, Ondrej and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Edge separators for graphs of bounded genus with applications},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {112},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {419--429},
      ISSN = {0304-3975},
}

@article {BPT06,
    AUTHOR = {B{\"o}r{\"o}czky, K{\'a}roly J. and Pach, J{\'a}nos and
              T{\'o}th, G{\'e}za},
     TITLE = {Planar crossing numbers of graphs embeddable in another
              surface},
   JOURNAL = {Internat. J. Found. Comput. Sci.},
  FJOURNAL = {International Journal of Foundations of Computer Science},
    VOLUME = {17},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {1005--1015},
      ISSN = {0129-0541},
}


@ARTICLE{CHS14,
   author = {Chimani, Markus and Hlin{\v{e}}n{\'y}, Petr and Salazar, Gelasio},
    title = "{Toroidal grid minors and stretch in embedded graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1403.1273},
    note = {\arxiv{1403.1273} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 05C62, 05C83, 05C85, 57M15, 68R10},
     year = 2014,
    month = mar,
}

@article {CHS20,
    AUTHOR = {Chimani, Markus and Hlin\v{e}n\'{y}, Petr and Salazar, Gelasio},
     TITLE = {Toroidal grid minors and stretch in embedded graphs},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {140},
      YEAR = {2020},
     PAGES = {323--371},
      ISSN = {0095-8956},
   MRCLASS = {05C10},
  MRNUMBER = {4033104},
       DOI = {10.1016/j.jctb.2019.05.009},
       URL = {https://doi.org/10.1016/j.jctb.2019.05.009},
}

@incollection {PT06a,
    AUTHOR = {Pach, J{\'a}nos and T{\'o}th, G{\'e}za},
     TITLE = {Crossing number of toroidal graphs},
 BOOKTITLE = {Topics in discrete mathematics},
    SERIES = {Algorithms Combin.},
    VOLUME = {26},
     PAGES = {581--590},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

%use GMS14
@unpublished{GMS1?,
 author = {Gutwenger, Carsten and Mutzel, Petra and Schaefer, Marcus},
 title = {Practical Experience with {H}anani-{T}utte  for Testing $c$-Planarity},
 note = {To be presented at ALENEX 2014.},
}

@inproceedings{GMS14,
    author = {Gutwenger, Carsten and Mutzel, Petra and Schaefer, Marcus},
  title     = {Practical Experience with {H}anani-{T}utte for Testing $c$-Planarity},
  year      = {2014},
  pages     = {86-97},
  ee        = {http://dx.doi.org/10.1137/1.9781611973198.9},
  crossref  = {McGM14},
}

@proceedings{McGM14,
  editor    = {Catherine C. McGeoch and
               Ulrich Meyer},
  booktitle     = {2014 Proceedings of the Sixteenth Workshop on Algorithm
               Engineering and Experiments (ALENEX)},
  publisher = {SIAM},
  year      = {2014},
  isbn      = {978-1-61197-319-8},
  ee        = {http://dx.doi.org/10.1137/1.9781611973198},
}


@inproceedings{SS13,
  author    = {Marcus Schaefer and
               Daniel {\v S}tefankovi{\v c}},
  title     = {Block Additivity of ${\ZN_2}$-Embeddings},
  booktitle = {Graph Drawing},
  year      = {2013},
  pages     = {185-195},
  ee        = {http://dx.doi.org/10.1007/978-3-319-03841-4_17},
  crossref  = {WW13},
}



@ARTICLE{FML14a,
   author = {Fabila-Monroy, Ruy and {L{\'o}pez}, Jorge},
    title = "{Computational search of small point sets with small rectilinear crossing number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1403.1288},
    note = {\arxiv{1403.1288} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
     year = 2014,
    month = mar,
 }

@article{FML14,
  author    = {Ruy Fabila Monroy and
               Jorge L{\'{o}}pez},
  title     = {Computational search of small point sets with small rectilinear crossing
               number},
  journal   = {J. Graph Algorithms Appl.},
  volume    = {18},
  number    = {3},
  pages     = {393--399},
  year      = {2014},
  url       = {http://dx.doi.org/10.7155/jgaa.00328},
  doi       = {10.7155/jgaa.00328},
  timestamp = {Thu, 20 Nov 2014 17:40:45 +0100},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/jgaa/MonroyL14},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@incollection{ALN14,
author={Angelini, Patrizio and Lozzo, Giordano and Neuwirth, Daniel},
title={On Some \cal{NP}-complete SEFE Problems},
year={2014},
isbn={978-3-319-04656-3},
booktitle={Algorithms and Computation},
volume={8344},
series={Lecture Notes in Computer Science},
editor={Pal, SudebkumarPrasant and Sadakane, Kunihiko},
doi={10.1007/978-3-319-04657-0_20},

url={http://dx.doi.org/10.1007/978-3-319-04657-0_20},
publisher={Springer International Publishing},

pages={200-212}
}

@article{ALN14b,
author={Angelini, Patrizio and Lozzo, Giordano and Neuwirth, Daniel},
title = "Advancements on \{SEFE\} and partitioned book embedding problems ",
journal = "Theoretical Computer Science ",
volume = "",
number = "0",
pages = " - ",
year = "2014",
note = "",
issn = "0304-3975",
doi = "http://dx.doi.org/10.1016/j.tcs.2014.11.016",
url = "http://www.sciencedirect.com/science/article/pii/S0304397514008597",
}

@incollection {W97,
    AUTHOR = {Wilf, Herbert S.},
     TITLE = {On crossing numbers, and some unsolved problems},
 BOOKTITLE = {Combinatorics, geometry and probability ({C}ambridge, 1993)},
     PAGES = {557--562},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {1997},
}

@article {SW94,
    AUTHOR = {Scheinerman, Edward R. and Wilf, Herbert S.},
     TITLE = {The rectilinear crossing number of a complete graph and
              {S}ylvester's ``four point problem'' of geometric probability},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {101},
      YEAR = {1994},
    NUMBER = {10},
     PAGES = {939--943},
      ISSN = {0002-9890},
}

@misc{T07a,
    author = "Terence Tao",
    title = "The crossing number inequality",
    howpublished = {\url{http://terrytao.wordpress.com/2007/09/18/the-crossing-number-inequality/} (last accessed 2014/4/18)},
}


%use HVLS17
@ARTICLE{HVLS14,
   author = {Hern\'{a}ndez-V\'{e}lez, C\'{e}sar. and Lea{\~n}os, Jes\'{u}s and {Salazar}, Gelasio},
    title = "{On the pseudolinear crossing number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1404.7332},
    note = {\arxiv{1404.7332} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 52C30, 68R10, 05C62},
     year = 2014,
    month = apr,
}

@article {HVLS17,
    AUTHOR = {Hern\'{a}ndez-V\'{e}lez, C\'{e}sar and Lea\~{n}os, Jes\'{u}s and Salazar, Gelasio},
     TITLE = {On the pseudolinear crossing number},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {84},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {297--310},
      ISSN = {0364-9024},
   MRCLASS = {05C62},
  MRNUMBER = {3601323},
MRREVIEWER = {Robert Cimikowski},
       DOI = {10.1002/jgt.22027},
       URL = {https://doi.org/10.1002/jgt.22027},
}

@book {F03,
    AUTHOR = {Finch, Steven R.},
     TITLE = {Mathematical constants},
    SERIES = {Encyclopedia of Mathematics and its Applications},
    VOLUME = {94},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2003},
     PAGES = {xx+602},
      ISBN = {0-521-81805-2},
}

@misc{EH14,
   author = "Eppstein, David and Huynh, Tony",
   title = "Bounds on chromatic number of $k$-planar graphs",
   year = "2014",
   note = "\url{http://mathoverflow.net/questions/168440/bounds-on-chromatic-number-of-k-planar-graphs} (Online; accessed 28-May-2014)",
 }

 @mastersthesis{S14b,
  title =	"The Cylindrical Crossing Number of the Complete Bipartite Graph",
  author =	"Sparks, Athena C.",
  month = "May",
  year = 	"2014",
  school = {California State University},
  address = {Northridge},
}

@inproceedings{FB04,
  author    = {Michael Forster and
               Christian Bachmaier},
  title     = {Clustered Level Planarity},
  booktitle = {SOFSEM},
  year      = {2004},
  pages     = {218-228},
  ee        = {http://dx.doi.org/10.1007/978-3-540-24618-3_18},
  crossref  = {EBPBS04},
}

@proceedings{EBPBS04,
  editor    = {Peter van Emde Boas and
               Jaroslav Pokorn{\'y} and
               M{\'a}ria Bielikov{\'a} and
               Julius Stuller},
  title     = {SOFSEM 2004: Theory and Practice of Computer Science, 30th
               Conference on Current Trends in Theory and Practice of Computer
               Science, Merin, Czech Republic, January 24-30, 2004},
  booktitle = {SOFSEM},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {2932},
  year      = {2004},
  isbn      = {3-540-20779-1},
}

@ARTICLE{ADLDBFR14,
   author = {Angelini, Patrizio and Da Lozzo, Giordano and Di Battista, Giuseppe and Frati, Fabrizio and Roselli, Vincenzo},
    title = "{On the Complexity of Clustered-Level Planarity and T-Level Planarity}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1406.6533},
    note = {\arxiv{1406.6533} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
 keywords = {Computer Science - Data Structures and Algorithms, Computer Science - Computational Geometry},
     year = 2014,
    month = jun,
}

%use DM16
@ARTICLE{DM14,
   author = {Dvo\v{r}\'{a}k, Zden\v{e}k and Mohar, Bojan},
    title = "{Crossing numbers of periodic graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1405.5117},
    note = {\arxiv{1405.5117} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10},
     year = 2014,
    month = may,
}

@article {DM16,
   author = {Dvo\v{r}\'{a}k, Zden\v{e}k and Mohar, Bojan},
     TITLE = {Crossing numbers of periodic graphs},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {83},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {34--43},
      ISSN = {0364-9024},
   MRCLASS = {05C10},
  MRNUMBER = {3529946},
MRREVIEWER = {R. Bruce Richter},
       DOI = {10.1002/jgt.21912},
       URL = {http://dx.doi.org/10.1002/jgt.21912},
}

@article{KU14,
  author    = {Kaufmann, Michael and
               Ueckerdt, Torsten},
  title     = {The Density of Fan-Planar Graphs},
  journal   = {CoRR},
  year      = {2014},
  volume    = {abs/1403.6184},
  url       = {http://arxiv.org/abs/1403.6184},
    note = {\arxiv{1403.6184} (last accessed 9/21/2017)},
}

@incollection{AS14,
 author = {Ackerman, Eyal and Schaefer, Marcus},
 title = {A crossing lemma for the pair-crossing number},
 crossref= {DS14},
     PAGES = {222--233},
}

@proceedings {DS14,
     TITLE = {Graph drawing},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {8871},
 BOOKTITLE = {Proceedings of the 22nd {I}nternational {S}ymposium ({GD}'14)
              {S}eptember 24--26, 2014},
    EDITOR = {Duncan, Christian and Symvonis, Antonios},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2014},
     PAGES = {ix+530},
}

%use CDMY16
@ARTICLE{CDMY14,
   author = {Cartwright, Dustin and Dudzik, Andrew and Manjunath, Madhusudan and Yao, Yuan},
    title = "{Embeddings and immersions of tropical curves}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1409.7372},
    note = {\arxiv{1409.7372} (last accessed 9/21/2017)},
     year = 2014,
    month = sep,
}

@article {CDMY16,
    AUTHOR = {Cartwright, Dustin and Dudzik, Andrew and Manjunath,
              Madhusudan and Yao, Yuan},
     TITLE = {Embeddings and immersions of tropical curves},
   JOURNAL = {Collect. Math.},
  FJOURNAL = {Collectanea Mathematica},
    VOLUME = {67},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {1--19},
      ISSN = {0010-0757},
   MRCLASS = {14T05},
  MRNUMBER = {3439837},
MRREVIEWER = {Simon Hampe},
       DOI = {10.1007/s13348-015-0149-8},
       URL = {http://dx.doi.org/10.1007/s13348-015-0149-8},
}

@misc{BJL14,
  author = {Bald, Samuel and Johnson, Matthew~P. and Liu, Ou},
  title = {Maximum Rectilinear Crossing Number},
  year = {2014},
  address = {University of Connecticut, US},
  howpublished = {Talk at 2014 Fall Workshop on Computational Geometry, University of Connecticut, US},
  url = {http://fwcg14.cse.uconn.edu/program/wp-content/uploads/sites/863/2014/10/fwcg2014_submission_29.pdf},
}

%use CFKUVW18
@article{CFKUVW17,
  author    = {Markus Chimani and
               Stefan Felsner and
               Stephen G. Kobourov and
               Torsten Ueckerdt and
               Pavel Valtr and
               Alexander Wolff},
  title     = {On the Maximum Crossing Number},
  journal   = {CoRR},
  volume    = {abs/1705.05176},
  year      = {2017},
  url       = {http://arxiv.org/abs/1705.05176},
    note = {\arxiv{1705.05176} (last accessed 9/21/2017)},
  timestamp = {Wed, 07 Jun 2017 14:40:23 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/corr/ChimaniFKUVW17},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}


@article {CFKUVW18,
    AUTHOR = {Chimani, Markus and Felsner, Stefan and Kobourov, Stephen and
              Ueckerdt, Torsten and Valtr, Pavel and Wolff, Alexander},
     TITLE = {On the maximum crossing number},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {22},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {67--87},
      ISSN = {1526-1719},
   MRCLASS = {05C10 (05C62 68Q25 68R10)},
  MRNUMBER = {3757346},
       DOI = {10.7155/jgaa.00458},
       URL = {https://doi.org/10.7155/jgaa.00458},
}

@article {FHL16,
    AUTHOR = {Feder, Elie and Harborth, Heiko and Lichter, Tamar},
     TITLE = {Maximum rectilinear crossing numbers for game board graphs},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {226},
      YEAR = {2016},
     PAGES = {87--102},
      ISSN = {0384-9864},
   MRCLASS = {05B45},
  MRNUMBER = {3642792},
}
	

%use CFGLMS15
@ARTICLE{CFGLMS14,
   author = {Chan, Timothy~M. and Frati, Fabrizio and Gutwenger, Carsten and Lubiw, Anna and
	Mutzel, Petra and Schaefer, Marcus},
    title = "{Drawing Partially Embedded and Simultaneously Planar Graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1410.8205},
    note = {\arxiv{1410.8205} (last accessed 9/21/2017)},
 primaryClass = "cs.CG",
 keywords = {Computer Science - Computational Geometry, Computer Science - Discrete Mathematics, Computer Science - Data Structures and Algorithms},
     year = 2014,
    month = oct,
}

@ARTICLE{GHLPRY14,
   author = {Gethner, Ellen and Hogben, Leslie and Lidick{\'y}, Bernard and Pfender, Florian and Ruiz, Amanda and Young, Michael},
   title = "{Crossing numbers of complete tripartite and balanced complete multipartite graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1410.0720},
    note = {\arxiv{1410.0720} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 05C35},
     year = 2014,
    month = oct,
}

@ARTICLE{GHLPRY17,
   author = {Gethner, Ellen and Hogben, Leslie and Lidick{\'y}, Bernard and Pfender, Florian and Ruiz, Amanda and Young, Michael},
     TITLE = {On crossing numbers of complete tripartite and balanced
              complete multipartite graphs},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {84},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {552--565},
      ISSN = {0364-9024},
   MRCLASS = {05C62 (05C10 68R10)},
  MRNUMBER = {3623394},
MRREVIEWER = {W. G. Brown},
       DOI = {10.1002/jgt.22041},
       URL = {http://dx.doi.org/10.1002/jgt.22041},
}

@ARTICLE{W14old,
   author = {Wang, Yi-Kai},
    title = "{Beyond Baker's Technique}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1412.0340},
    note = {\arxiv{1412.0340} (last accessed 9/21/2017)},
     year = 2014,
    month = nov,
}

@ARTICLE{W14,
   author = {{Wang}, Yi-Kai},
    title = "{MAX-CSP, Graph Cuts and Statistical Physics}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1412.0340},
    note = {\arxiv{1412.0340} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
 keywords = {Computer Science - Data Structures and Algorithms},
     year = 2014,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1412.0340W},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {BFH13,
    AUTHOR = {Bode, Jens-P. and Feder, Elie and Harborth, Heiko},
     TITLE = {Extremal values of the maximum rectilinear crossing numbers of
              $2$-regular graphs},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {69},
      YEAR = {2013},
     PAGES = {95--100},
      ISSN = {1183-1278},
}

@article{ABGR15,
  title={1-Planarity of Graphs with a Rotation System},
  author={Auer, Christopher and Brandenburg, Franz J and Glei{\ss}ner, Andreas and Reislhuber, Josef},
   journal = {Journal of Graph Algorithms and Applications},
   year = {2015},
   volume = {19},
   number = {1},
   pages = {67--86},
   doi = {10.7155/JGAA.00347}
}

@article {H71,
    AUTHOR = {Harborth, Heiko},
     TITLE = {{\"U}ber die {K}reuzungszahl vollst{\"a}ndiger, {$n$}-geteilter
              {G}raphen},
   JOURNAL = {Math. Nachr.},
  FJOURNAL = {Mathematische Nachrichten},
    VOLUME = {48},
      YEAR = {1971},
     PAGES = {179--188},
      ISSN = {0025-584X},
}

@article {HM74,
    AUTHOR = {Harborth, Heiko and Mengersen, Ingrid},
     TITLE = {Edges without crossings in drawings of complete graphs},
   JOURNAL = {J. Combinatorial Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {17},
      YEAR = {1974},
     PAGES = {299--311},
}

@article {M78,
    AUTHOR = {Mengersen, Ingrid},
     TITLE = {Die {M}aximalzahl von kreuzungsfreien {K}anten in
              {D}arstellungen von vollst\"{a}ndigen {$n$}-geteilten {G}raphen},
   JOURNAL = {Math. Nachr.},
  FJOURNAL = {Mathematische Nachrichten},
    VOLUME = {85},
      YEAR = {1978},
     PAGES = {131--139},
      ISSN = {0025-584X},
}

@inproceedings {HT96,
    AUTHOR = {Harborth, Heiko and Th{\"u}rmann, Christian},
     TITLE = {Numbers of edges without crossings in rectilinear drawings of
              the complete graph},
 BOOKTITLE = {Proceedings of the {T}wenty-seventh {S}outheastern
              {I}nternational {C}onference on {C}ombinatorics, {G}raph
              {T}heory and {C}omputing ({B}aton {R}ouge, {LA}, 1996)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {119},
      YEAR = {1996},
     PAGES = {79--83},
      ISSN = {0384-9864},
}

%also see BBKR15a
@ARTICLE{BBKR15,
   author = {{Bekos}, Michael~A. and {Bruckdorfer}, Till and {Kaufmann}, Michael and
	{Raftopoulou}, Chrysanthi~N.},
    title = "{The Book Thickness of $1$-Planar Graphs is Constant}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1503.04990},
    note = {\arxiv{1503.04990} (last accessed 9/21/2017)},
     year = 2015,
    month = mar,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150304990B},
}

@article {BBKR17,
    AUTHOR = {Bekos, Michael A. and Bruckdorfer, Till and Kaufmann, Michael
              and Raftopoulou, Chrysanthi N.},
     TITLE = {The book thickness of 1-planar graphs is constant},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {79},
      YEAR = {2017},
    NUMBER = {2},
     PAGES = {444--465},
      ISSN = {0178-4617},
   MRCLASS = {05C85 (05C10 68R10)},
  MRNUMBER = {3681405},
       DOI = {10.1007/s00453-016-0203-2},
       URL = {http://dx.doi.org/10.1007/s00453-016-0203-2},
}



@inproceedings{BBKR15a,
   author = {{Bekos}, Michael~A. and {Bruckdorfer}, Till and {Kaufmann}, Michael and
	{Raftopoulou}, Chrysanthi~N.},
  title     = {1-Planar Graphs have Constant Book Thickness},
  booktitle = {Algorithms - {ESA} 2015 - 23rd Annual European Symposium, Patras,
               Greece, September 14-16, 2015, Proceedings},
  pages     = {130--141},
  year      = {2015},
  crossref  = {BF15},
  url       = {http://dx.doi.org/10.1007/978-3-662-48350-3_12},
  doi       = {10.1007/978-3-662-48350-3_12},
  timestamp = {Wed, 02 Sep 2015 16:09:00 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/esa/BekosB0R15},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@proceedings{BF15,
  editor    = {Nikhil Bansal and
               Irene Finocchi},
  title     = {Algorithms - {ESA} 2015 - 23rd Annual European Symposium, Patras,
               Greece, September 14-16, 2015, Proceedings},
  series    = {Lecture Notes in Computer Science},
  volume    = {9294},
  publisher = {Springer},
  year      = {2015},
  url       = {http://dx.doi.org/10.1007/978-3-662-48350-3},
  doi       = {10.1007/978-3-662-48350-3},
  isbn      = {978-3-662-48349-7},
  timestamp = {Wed, 02 Sep 2015 16:08:20 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/esa/2015},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}


%use MPR16
@ARTICLE{MPR13,
   author = {{McQuillan}, Dan and {Pan}, Shengjun and {Richter}, R.~Bruce},
    title = "{On the crossing number of $K_{13}$}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1307.3297},
    note = {\arxiv{1307.3297} (last accessed 9/21/2017)},
     year = 2013,
    month = jul,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1307.3297M},
}

@article {MR16,
    AUTHOR = {McQuillan, Dan and Richter, R. Bruce},
     TITLE = {On the crossing number of {$K_n$} without computer assistance},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {82},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {387--432},
      ISSN = {0364-9024},
   MRCLASS = {05C62 (05C10)},
  MRNUMBER = {3515575},
MRREVIEWER = {John Baptist Gauci},
       DOI = {10.1002/jgt.21908},
       URL = {http://dx.doi.org/10.1002/jgt.21908},
}

%use MR16 instead
@article {MR15,
author = {McQuillan, Dan and Richter, R. Bruce},
title = {On the Crossing Number of {$K_n$} without Computer Assistance},
journal = {Journal of Graph Theory},
issn = {1097-0118},
url = {http://dx.doi.org/10.1002/jgt.21908},
doi = {10.1002/jgt.21908},
keywords = {crossing number, complete graph},
year = {2015},
}

@article {MPR15,
    AUTHOR = {McQuillan, Dan and Pan, Shengjun and Richter, R. Bruce},
     TITLE = {On the crossing number of {$K_{13}$}},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {115},
      YEAR = {2015},
     PAGES = {224--235},
      ISSN = {0095-8956},
   MRCLASS = {05C62 (05C10 68R10)},
  MRNUMBER = {3383258},
MRREVIEWER = {Gelasio Salazar},
       DOI = {10.1016/j.jctb.2015.06.002},
       URL = {https://doi.org/10.1016/j.jctb.2015.06.002},
}

@unpublished{PSTT15,
  author =       "Pach, J{\'a}nos and Sz{\'e}kely, L{\'a}szl{\'o} A. and T{\'o}th, Csaba and T{\'o}th, G{\'e}za",
  title =        "Note on k-planar crossing numbers",
  note = "Submitted to {\em Computational Geometry: Theory and Applications}. Special Issue in Memoriam Ferran Hurtado",
}

@article {HK93,
    AUTHOR = {Harary, Frank and Kainen, Paul C.},
     TITLE = {The cube of a path is maximal planar},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {7},
      YEAR = {1993},
     PAGES = {55--56},
      ISSN = {1183-1278},
}

@article {HKR99,
    AUTHOR = {Harary, Frank and Kainen, Paul C. and Riskin, Adrian},
     TITLE = {Every graph of cyclic bandwidth 3 is toroidal},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {27},
      YEAR = {1999},
     PAGES = {81--84},
      ISSN = {1183-1278},
}

%use DEW17
@ARTICLE{DEW15,
   author = {{Dujmovi{\'c}}, Vida and {Eppstein}, David and {Wood}, David~R.},
    title = "{Genus, Treewidth, and Local Crossing Number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1506.04380},
    note = {\arxiv{1506.04380} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Computational Geometry, Computer Science - Discrete Mathematics},
     year = 2015,
    month = jun,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150604380D},
}

@incollection {DEW15a,
   author = {{Dujmovi{\'c}}, Vida and {Eppstein}, David and {Wood}, David~R.},
    title = "{Genus, Treewidth, and Local Crossing Number}",
 BOOKTITLE = {Graph drawing and network visualization},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9411},
     PAGES = {87--98},
 PUBLISHER = {Springer, Cham},
      YEAR = {2015},
   MRCLASS = {05C62},
  MRNUMBER = {3487155},
       DOI = {10.1007/978-3-319-27261-0_8},
       URL = {https://doi.org/10.1007/978-3-319-27261-0_8},
}

@article{DEW17,
  author    = {Vida Dujmovi\'{c} and
               David Eppstein and
               David R. Wood},
    title = {Structure of Graphs with Locally Restricted Crossings},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    volume = {31},
    number = {2},
    pages = {805-824},
    year = {2017},
    doi = {10.1137/16M1062879},

    URL = {http://dx.doi.org/10.1137/16M1062879},
    eprint = {http://dx.doi.org/10.1137/16M1062879},
}

@article {G78,
    AUTHOR = {Gross, Jonathan L.},
     TITLE = {An infinite family of octahedral crossing numbers},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {2},
      YEAR = {1978},
    NUMBER = {2},
     PAGES = {171--178},
      ISSN = {0364-9024},
}

@article {T97,
    AUTHOR = {Thomassen, Carsten},
     TITLE = {The genus problem for cubic graphs},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {69},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {52--58},
      ISSN = {0095-8956},
}


@article {T89,
    AUTHOR = {Thomassen, Carsten},
     TITLE = {The graph genus problem is {NP}-complete},
   JOURNAL = {J. Algorithms},
  FJOURNAL = {Journal of Algorithms},
    VOLUME = {10},
      YEAR = {1989},
    NUMBER = {4},
     PAGES = {568--576},
      ISSN = {0196-6774},
}

@ARTICLE{S06,
   author = {{Sulanke}, Thom},
    title = "{Irreducible triangulations of low genus surfaces}",
  journal = {ArXiv Mathematics e-prints},
   eprint = {math/0606690},
      note = {\arxiv{0606690} (last accessed 9/21/2017)},
 keywords = {Mathematics - Combinatorics, 05c30, 05c10},
     year = 2006,
    month = jun,
}

@book {EK68,
     TITLE = {Theory of graphs},
     editor = {Erd\H{o}s, Paul and Katona, Gyula},
    SERIES = {Proceedings of the Colloquium held at Tihany, Hungary,
              September},
    VOLUME = {1966},
 PUBLISHER = {Academic Press, New York-London; Akad\'emiai Kiad\'o,
              Budapest},
      YEAR = {1968},
     PAGES = {370},
   MRCLASS = {05.40},
  MRNUMBER = {0232693 (38 \#1016)},
}

@article {HSMV15,
    AUTHOR = {He, Hongmei and S{\u{a}}l{\u{a}}gean, Ana and M{\"a}kinen,
              Erkki and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {Various heuristic algorithms to minimise the two-page crossing numbers of graphs},
   JOURNAL = {Open Comput. Sci.},
  FJOURNAL = {Open Computer Science},
    VOLUME = {5},
      YEAR = {2015},
      pages = {22-40},
    NUMBER = {1},
      ISSN = {2299-1093},
}

%use KNPSS15b
@ARTICLE{KNPSS15,
   author = {{Kostitsyna}, Irina and {N{\"o}llenburg}, Martin and {Polishchuk}, Valentin and
	{Schulz}, Andr{\'e} and {Strash}, Darren},
    title = "{On Minimizing Crossings in Storyline Visualizations}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1509.00442},
      note = {\arxiv{1509.00442} (last accessed 9/21/2017)},
 primaryClass = "cs.DS",
     year = 2015,
    month = sep,
}

@inproceedings{KNPSS15b,
   author = {{Kostitsyna}, Irina and {N{\"o}llenburg}, Martin and {Polishchuk}, Valentin and
	{Schulz}, Andr{\'e} and {Strash}, Darren},
     TITLE = {On minimizing crossings in storyline visualizations},
 BOOKTITLE = {Graph drawing and network visualization},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9411},
     PAGES = {192--198},
 PUBLISHER = {Springer, Cham},
      YEAR = {2015},
   MRCLASS = {68R10 (00A99 05C90)},
  MRNUMBER = {3487163},
       DOI = {10.1007/978-3-319-27261-0_16},
       URL = {http://dx.doi.org/10.1007/978-3-319-27261-0_16},
}

@Article{CG15,
   author = {{Markus} {Chimani} and {Carsten} {Gutwenger}},
   title = {Hypergraph and Minor Crossing Number Problems},
   journal = {Journal of Graph Algorithms and Applications},
   year = {2015},
   volume = {19},
   number = {1},
   pages = {191--222},
   doi = {10.7155/jgaa.00353}
}



@InProceedings{BK15,
  title =	"Bounding the pseudolinear crossing number of {$K_n$} via simulated annealing",
  author =	"{Balko}, Martin and {Kyn{\v c}l}, Jan",
  booktitle =	"Abstracts XVI Spanish Meeting on Computational Geometry",

  year = 	"2015",

  editor =	"Ramos, Pedro and Silveira, Rodrigo I.",

  pages =	"37--40",
  url = "http://www-ma2.upc.es/egc15/wp-content/uploads/2013/10/AbstractsXVIEGC.pdf",
}

@InProceedings{LRMZ15,
  title =	"Grundy and pseudo-Grundy indices for complete geometric graphs",
  author =	"Lara, D. and Rubio-Montiel, C. and Zaragoza, F.",
  booktitle =	"Abstracts XVI Spanish Meeting on Computational Geometry",

  year = 	"2015",

  editor =	"Ramos, Pedro and Silveira, Rodrigo I.",

  pages =	"73--76",
  url = "http://www-ma2.upc.es/egc15/wp-content/uploads/2013/10/AbstractsXVIEGC.pdf",
}

@article {GM14,
    AUTHOR = {Ginn, Mark and Miller, Faith},
     TITLE = {The crossing number of {$K_{3,3,n}$}},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {221},
      YEAR = {2014},
     PAGES = {49--54},
      ISSN = {0384-9864},
}


@article {HT14,
    AUTHOR = {Harborth, Heiko and Th{\"u}rmann, Christian},
     TITLE = {Maximum rectilinear crossing number in drawings of the
              complete graph with a given convex hull},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {221},
      YEAR = {2014},
     PAGES = {121--127},
      ISSN = {0384-9864},
}

@article {BFHHL14,
    AUTHOR = {Bode, Jens-P. and Feder, Elie and Harborth, Heiko and
              Horowitz, David and Lichter, Tamar},
     TITLE = {Extremal values of the maximum rectilinear crossing number of
              cycles with diagonals},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {220},
      YEAR = {2014},
     PAGES = {33--48},
      ISSN = {0384-9864},
}

@article {BGGP10,
    AUTHOR = {Beaudou, Laurent and Gerbaud, Antoine and Grappe, Roland and
              Palesi, Fr{\'e}d{\'e}ric},
     TITLE = {Drawing disconnected graphs on the {K}lein bottle},
   JOURNAL = {Graphs Combin.},
  FJOURNAL = {Graphs and Combinatorics},
    VOLUME = {26},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {471--481},
      ISSN = {0911-0119},
     CODEN = {GRCOE5},
   MRCLASS = {05C62 (05C10)},
  MRNUMBER = {2669452},
       DOI = {10.1007/s00373-010-0928-7},
       URL = {http://dx.doi.org/10.1007/s00373-010-0928-7},
}

@article{CMS15,
    author = "Cabello, Sergio and Mohar, Bojan and {\v{S}}{\'a}mal, Robert",
    title = "Drawing a disconnected graph on the torus (Extended abstract) ",
    journal = "Electronic Notes in Discrete Mathematics ",
    volume = "49",
    number = "",
    pages = "779 - 786",
    year = "2015",
    note = "The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015 ",
    issn = "1571-0653",
    doi = "http://dx.doi.org/10.1016/j.endm.2015.06.105",
    url = "http://www.sciencedirect.com/science/article/pii/S1571065315001511",
}

@Article{CFGLMS15,
   author = {Chan, {Timothy} {M}. and Frati, {Fabrizio} and Gutwenger, Carsten and Lubiw, Anna and Mutzel, Petra and Schaefer, Marcus},
   title = {Drawing Partially Embedded and Simultaneously Planar Graphs},
   journal = {Journal of Graph Algorithms and Applications},
   year = {2015},
   volume = {19},
   number = {2},
   pages = {681--706},
   doi = {10.7155/jgaa.00375}
}

@Inbook{HS15,
    author="Hlin{\v{e}}n{\'y}, Petr and Salazar, Gelasio",
    editor="Elbassioni, Khaled and Makino, Kazuhisa",
    chapter="On Hardness of the Joint Crossing Number",
    title="Algorithms and Computation: 26th International Symposium, ISAAC 2015, Nagoya, Japan, December 9-11, 2015, Proceedings",
    year="2015",
    publisher="Springer Berlin Heidelberg",
    address="Berlin, Heidelberg",
    pages="603--613",
    isbn="978-3-662-48971-0",
    doi="10.1007/978-3-662-48971-0_51",
    url="http://dx.doi.org/10.1007/978-3-662-48971-0_51"
}

@article{AAFMMMMRRV15,
  author = {\'{A}brego, Bernardo M. and Aichholzer, Oswin and Fern\'{a}ndez-Merchant, Silvia  and McQuillan, Dan and Mohar, Bojan and Mutzel, Petra and Ramos, Pedro and Richter, R. Bruce and Vogtenhuber, Birgit},
  ee = {http://arxiv.org/abs/1510.00549},
    note = {\arxiv{1510.00549} (last accessed 9/21/2017)},
  journal = {CoRR},
  keywords = {dblp},
  title = {Bishellable drawings of $K_n$},
  url = {http://dblp.uni-trier.de/db/journals/corr/corr1510.html#AbregoAFMMM0RV15},
  volume = {abs/1510.00549},
  year = 2015
}



@inproceedings{SS15,
  author    = {Marcus Schaefer and
               Daniel Stefankovic},
  title     = {The Degenerate Crossing Number and Higher-Genus Embeddings},
  booktitle = {Graph Drawing and Network Visualization - 23rd International Symposium,
               {GD} 2015, Los Angeles, CA, USA, September 24-26, 2015, Revised Selected
               Papers},
  pages     = {63--74},
  year      = {2015},
  crossref  = {DBLP:conf/gd/2015},
  url       = {http://dx.doi.org/10.1007/978-3-319-27261-0_6},
  doi       = {10.1007/978-3-319-27261-0_6},
  timestamp = {Wed, 16 Dec 2015 12:56:13 +0100},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/gd/SchaeferS15},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@proceedings{DBLP:conf/gd/2015,
  editor    = {Emilio Di Giacomo and
               Anna Lubiw},
  title     = {Graph Drawing and Network Visualization - 23rd International Symposium,
               {GD} 2015, Los Angeles, CA, USA, September 24-26, 2015, Revised Selected
               Papers},
  series    = {Lecture Notes in Computer Science},
  volume    = {9411},
  publisher = {Springer},
  year      = {2015},
  url       = {http://dx.doi.org/10.1007/978-3-319-27261-0},
  doi       = {10.1007/978-3-319-27261-0},
  isbn      = {978-3-319-27260-3},
  timestamp = {Wed, 16 Dec 2015 12:45:26 +0100},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/gd/2015},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@article {BH05,
    AUTHOR = {Buchheim, Christoph and Hong, Seok-Hee},
     TITLE = {Crossing minimization for symmetries},
   JOURNAL = {Theory Comput. Syst.},
  FJOURNAL = {Theory of Computing Systems},
    VOLUME = {38},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {293--311},
      ISSN = {1432-4350},
     CODEN = {TCSYFI},
   MRCLASS = {05C10 (05C62 68Q17 68R10)},
  MRNUMBER = {2130893},
MRREVIEWER = {Gelasio Salazar},
       DOI = {10.1007/s00224-005-1142-5},
       URL = {http://dx.doi.org/10.1007/s00224-005-1142-5},
}

%use B18
@article{B16,
  author    = {Franz J. Brandenburg},
  title     = {A Reduction System for Optimal 1-Planar Graphs},
  journal   = {CoRR},
  volume    = {abs/1602.06407},
  year      = {2016},
  url       = {http://arxiv.org/abs/1602.06407},
    note = {\arxiv{1602.06407} (last accessed 9/21/2017)},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/corr/Brandenburg16},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@article {B18,
    AUTHOR = {Brandenburg, Franz J.},
     TITLE = {Recognizing optimal 1-planar graphs in linear time},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {80},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {1--28},
      ISSN = {0178-4617},
   MRCLASS = {05C62 (68R10)},
  MRNUMBER = {3741533},
       DOI = {10.1007/s00453-016-0226-8},
       URL = {https://doi.org/10.1007/s00453-016-0226-8},
}



@inproceedings{HD16,
  author    = {Petr Hlinen{\'{y}} and
               Marek Dern{\'{a}}r},
  title     = {Crossing Number is Hard for Kernelization},
  booktitle = {32nd International Symposium on Computational Geometry, SoCG 2016,
               June 14-18, 2016, Boston, MA, {USA}},
  pages     = {42:1--42:10},
  year      = {2016},
  crossref  = {FL16},
  url       = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.42},
  doi       = {10.4230/LIPIcs.SoCG.2016.42},

}

@proceedings{FL16,
  editor    = {S{\'{a}}ndor P. Fekete and
               Anna Lubiw},
  title     = {32nd International Symposium on Computational Geometry, SoCG 2016,
               June 14-18, 2016, Boston, MA, {USA}},
  series    = {LIPIcs},
  volume    = {51},
  publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
  year      = {2016},
  url       = {http://www.dagstuhl.de/dagpub/978-3-95977-009-5},
  isbn      = {978-3-95977-009-5},

}

@ARTICLE{CdC16,
   author = {{Carpentier}, Sylvain and {del Campo}, Adan Medrano Martin},
    title = "{Tropical Embeddings of Metric Graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1604.06176},
      note = {\arxiv{1604.06176} (last accessed 9/21/2017)},
     year = 2016,
    month = apr,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160406176D},

}

%use FPS16b
@ARTICLE{FPS16,
   author = {{Fox}, Jacob and {Pach}, J\'{a}nos and {Suk}, Andrew},
    title = "{Approximating the rectilinear crossing number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1606.03753},
      note = {\arxiv{1606.03753} (last accessed 9/21/2017)},
 keywords = {Computer Science - Computational Geometry, Mathematics - Combinatorics},
     year = 2016,
    month = jun,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160603753F},
}

@incollection {FPS16b,
   author = {{Fox}, Jacob and {Pach}, J\'{a}nos and {Suk}, Andrew},
     TITLE = {Approximating the rectilinear crossing number},
 BOOKTITLE = {Graph drawing and network visualization},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9801},
     PAGES = {413--426},
 PUBLISHER = {Springer, Cham},
      YEAR = {2016},
   MRCLASS = {68R10 (05C62)},
  MRNUMBER = {3627103},
}

@misc{DGM16,
 author = {Stephane Durocher and Ellen Gethnery and Debajyoti Mondalz},
 title = {On the Biplanar Crossing Number of {$K_n$}},
 howpublished = {Accepted to CCCG 2016, Vancouver, British Columbia. Available at \url{http://www.cs.umanitoba.ca/~durocher/research/pubs/durocherCCCG2016.pdf} (last accessed 7/19/2016)},
 year = {2016},
}


@ARTICLE{FSM16,
   author = {{Fatemi}, Zahra and {Salehi}, Mostafa and {Magnani}, Matteo},
    title = "{A simple multiforce layout for multiplex networks}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1607.03914},
      note = {\arxiv{1607.03914} (last accessed 9/21/2017)},
 keywords = {Computer Science - Social and Information Networks, Physics - Physics and Society},
     year = 2016,
    month = jul,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160703914F},

}

@inproceedings{BJL16,
  author    = {Samuel Bald and
               Matthew P. Johnson and
               Ou Liu},
  title     = {Approximating the Maximum Rectilinear Crossing Number},
  booktitle = {Computing and Combinatorics - 22nd International Conference, {COCOON}
               2016, Ho Chi Minh City, Vietnam, August 2-4, 2016, Proceedings},
  pages     = {455--467},
  year      = {2016},
  crossref  = {DBLP:conf/cocoon/2016},
  url       = {http://dx.doi.org/10.1007/978-3-319-42634-1_37},
  doi       = {10.1007/978-3-319-42634-1_37},
  timestamp = {Wed, 20 Jul 2016 14:49:40 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/cocoon/BaldJL16},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@proceedings{DBLP:conf/cocoon/2016,
  editor    = {Thang N. Dinh and
               My T. Thai},
  title     = {Computing and Combinatorics - 22nd International Conference, {COCOON}
               2016, Ho Chi Minh City, Vietnam, August 2-4, 2016, Proceedings},
  series    = {Lecture Notes in Computer Science},
  volume    = {9797},
  publisher = {Springer},
  year      = {2016},
  url       = {http://dx.doi.org/10.1007/978-3-319-42634-1},
  doi       = {10.1007/978-3-319-42634-1},
  isbn      = {978-3-319-42633-4},
  timestamp = {Wed, 20 Jul 2016 14:47:18 +0200},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/cocoon/2016},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

%use AFM17
@ARTICLE{AFM15,
   author = {{{\'A}brego}, Bernardo~M. and {Fern{\'a}ndez-Merchant}, Silvia},
    title = "{The rectilinear local crossing number of $K_n$}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1508.07926},
      note = {\arxiv{1508.07926} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 05C62, 52C10, 68R10},
     year = 2015,
    month = aug,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150807926A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{ADFMLSS17,
  title={On the Rectilinear Local Crossing Number of {$K_{m,n}$}},
  author={{{\'A}brego}, Bernardo~M. and  Dondzila,Kory and
  {Fern{\'a}ndez-Merchant}, Silvia and  Lagoda, Evgeniya and  Sajjadi, Seyed and  Sapozhnikov, Yakov},
  journal={Journal of Information Processing},
  volume={25},
  number={ },
  pages={542-550},
  month= {August},
  year={2017},
  doi={10.2197/ipsjjip.25.542}
}

%use DGAHVLM18
@ARTICLE{DGAHVLM17,
   author = {{Duque}, Frank and {Gonz{\'a}lez-Aguilar}, Hern\'{a}n and {Hern{\'a}ndez-V{\'e}lez}, C\'{e}sar and
	{Lea{\~n}os}, Jes\'{u}s and {Medina}, Carolina},
    title = "{The complexity of computing the cylindrical and the $t$-circle crossing number of a graph}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1708.01942},
      note = {\arxiv{1708.01942} (last accessed 9/21/2017)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 68R10, 05C85},
     year = 2017,
    month = aug,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170801942D},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{DGAHVLM18,
   author = {{Duque}, Frank and {Gonz{\'a}lez-Aguilar}, Hern\'{a}n and {Hern{\'a}ndez-V{\'e}lez}, C\'{e}sar and
	{Lea{\~n}os}, Jes\'{u}s and {Medina}, Carolina},
     TITLE = {The complexity of computing the cylindrical and the
              {$t$}-circle crossing number of a graph},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {25},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {Paper 2.43, 11},
      ISSN = {1077-8926},
   MRCLASS = {68R10 (05C10 05C85 68Q17)},
  MRNUMBER = {3814277},
}


@book{A96,
author = {Arnold, Englebert},
title = {Die Ankerwicklungen und Ankerkonstruktionen der Gleichstrom-Dynamomaschinen},
publisher = {Springer},
address = {Berlin},
pages = {312},
year = {1896},
edition = {2nd edition},
}

@book{C85,
    author = {Clifford, William Kingdon},
    title = {The common sense of the exact sciences},
    publisher = {Appleton},
    address = {New York},
    pages = 271,
    year = 1885,

}



@incollection {MUV02,
    AUTHOR = {Mu{\~{n}}oz, Xavier and Unger, Walter and V{\v{r}}{\v{t}}o, Imrich},
     TITLE = {One sided crossing minimization is {NP}-hard for sparse
              graphs},
 BOOKTITLE = {Graph drawing ({V}ienna, 2001)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2265},
     PAGES = {115--123},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2002},
   MRCLASS = {68R10 (05C85 68Q17 68W35)},
  MRNUMBER = {1962424},
       DOI = {10.1007/3-540-45848-4_10},
       URL = {https://doi.org/10.1007/3-540-45848-4_10},
}

@ARTICLE{FHKLSS18,
   author = {{Fallon}, Joshua and {Hogenson}, Kirsten and {Keough}, Lauren and {Lomel{\'{\i}}}, Mario and
	{Schaefer}, Marcus and {Sober{\'o}n}, Pablo},
    title = "{A Note on the Maximum Rectilinear Crossing Number of Spiders}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2018},
  volume    = {abs/1808.00385},
  url       = {http://arxiv.org/abs/1808.00385},
    note = {\arxiv{1808.00385} (last accessed 10/15/2018)},
}

%use BETF19
@ARTICLE{BETF18,
   author = {{Bennett}, Patrick and {English}, Sean and {Talanda-Fisher}, Maria},
    title = "{Weighted Turan Problems with Applications}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2018},
   eprint = {1809.05028},
  volume    = {abs/1809.05028},
  url       = {http://arxiv.org/abs/1809.05028},
    note = {\arxiv{1809.05028} (last accessed 10/15/2018)},
}

@article {BETF19,
    AUTHOR = {Bennett, Patrick and English, Sean and Talanda-Fisher, Maria},
     TITLE = {Weighted {T}ur\'{a}n problems with applications},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {342},
      YEAR = {2019},
    NUMBER = {8},
     PAGES = {2165--2172},
      ISSN = {0012-365X},
   MRCLASS = {05C35 (05C22)},
  MRNUMBER = {3952133},
MRREVIEWER = {Arran Hamm},
       DOI = {10.1016/j.disc.2019.04.007},
       URL = {https://doi.org/10.1016/j.disc.2019.04.007},
}

@article {S97,
    AUTHOR = {Sz\'{e}kely, L\'{a}szl\'{o} A.},
     TITLE = {Crossing numbers and hard {Erd\H{o}s} problems in discrete
              geometry},
   JOURNAL = {Combin. Probab. Comput.},
  FJOURNAL = {Combinatorics, Probability and Computing},
    VOLUME = {6},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {353--358},
      ISSN = {0963-5483},
   MRCLASS = {52C10 (05C10)},
  MRNUMBER = {1464571},
MRREVIEWER = {W. Moser},
       DOI = {10.1017/S0963548397002976},
       URL = {https://doi.org/10.1017/S0963548397002976},
}

@incollection {PT18,
    AUTHOR = {Pach, {J\'{a}nos} and T\'{o}th, {G\'{e}za}},
     TITLE = {A crossing lemma for multigraphs},
 BOOKTITLE = {34th {I}nternational {S}ymposium on {C}omputational
              {G}eometry},
    SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
    VOLUME = {99},
     PAGES = {Art. No. 65, 13},
 PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
      YEAR = {2018},
   MRCLASS = {05C62},
  MRNUMBER = {3824309},
}

%use KPTU18b
@ARTICLE{KPTU18,
   author = {{Kaufmann}, Michael and Pach, {J\'{a}nos} and T\'{o}th, {G\'{e}za} and {Ueckerdt}, Torsten
	},
    title = "{The number of crossings in multigraphs with no empty lens}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2018},
  volume    = {abs/1808.10480},
  url       = {http://arxiv.org/abs/1808.10480},
    note = {\arxiv{1808.10480} (last accessed 10/15/2018)},
}

@incollection {KPTU18b,
    AUTHOR = {Kaufmann, Michael and Pach, J\'{a}nos and T\'{o}th, G\'{e}za and Ueckerdt,
              Torsten},
     TITLE = {The number of crossings in multigraphs with no empty lens},
 BOOKTITLE = {Graph drawing and network visualization},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {11282},
     PAGES = {242--254},
 PUBLISHER = {Springer, Cham},
      YEAR = {2018},
   MRCLASS = {68R10},
  MRNUMBER = {3901462},
}

@article {ADHJ19,
    AUTHOR = {Asplund, John and Do, Thao and Hamm, Arran and Jain, Vishesh},
     TITLE = {On the {$k$}-planar local crossing number},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {342},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {927--933},
      ISSN = {0012-365X},
   MRCLASS = {05C62 (05C10)},
  MRNUMBER = {3894102},
       DOI = {10.1016/j.disc.2018.11.020},
       URL = {https://doi.org/10.1016/j.disc.2018.11.020},
}


@article {ADHSTW18,
    AUTHOR = {Asplund, John and Do, Thao and Hamm, Arran and Sz\'{e}kely, L\'{a}szl\'{o}
              and Taylor, Libby and Wang, Zhiyu},
     TITLE = {{$k$}-planar crossing number of random graphs and random
              regular graphs},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {247},
      YEAR = {2018},
     PAGES = {419--422},
      ISSN = {0166-218X},
   MRCLASS = {05C10 (05C62 05C80)},
  MRNUMBER = {3843355},
       DOI = {10.1016/j.dam.2018.04.007},
       URL = {https://doi.org/10.1016/j.dam.2018.04.007},
}


@incollection {S04b,
    AUTHOR = {Spencer, Joel},
     TITLE = {The biplanar crossing number of the random graph},
 BOOKTITLE = {Towards a theory of geometric graphs},
    SERIES = {Contemp. Math.},
    VOLUME = {342},
     PAGES = {269--271},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2004},
   MRCLASS = {05C10 (05C80)},
  MRNUMBER = {2065270},
MRREVIEWER = {Lauren\c{t}iu Modan},
       DOI = {10.1090/conm/342/06147},
       URL = {https://doi.org/10.1090/conm/342/06147},
}

@article {CG18,
    AUTHOR = {Clark, Gregory J. and Spencer, Gwen},
     TITLE = {New bounds on the biplanar crossing number of low-dimensional
              hypercubes: how low can you go?},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {83},
      YEAR = {2018},
     PAGES = {52--60},
      ISSN = {1183-1278},
   MRCLASS = {05C62 (05C35)},
  MRNUMBER = {3821098},
}

@article {PSTT18,
    AUTHOR = {Pach, J\'{a}nos and Sz\'{e}kely, L\'{a}szl\'{o} A. and T\'{o}th, Csaba D. and
              T\'{o}th, G\'{e}za},
     TITLE = {Note on {$k$}-planar crossing numbers},
   JOURNAL = {Comput. Geom.},
  FJOURNAL = {Computational Geometry. Theory and Applications},
    VOLUME = {68},
      YEAR = {2018},
     PAGES = {2--6},
      ISSN = {0925-7721},
   MRCLASS = {68R10},
  MRNUMBER = {3715039},
       DOI = {10.1016/j.comgeo.2017.06.015},
       URL = {https://doi.org/10.1016/j.comgeo.2017.06.015},
}

@article {CSW17,
    AUTHOR = {Czabarka, \'{E}va and Sz\'{e}kely, L\'{a}szl\'{o} A. and Wagner, Stephan},
     TITLE = {Inducibility in binary trees and crossings in random
              tanglegrams},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {31},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {1732--1750},
      ISSN = {0895-4801},
   MRCLASS = {05C05 (05C62 05D40 92D15)},
  MRNUMBER = {3686790},
MRREVIEWER = {Robert Cimikowski},
       DOI = {10.1137/16M1060741},
       URL = {https://doi.org/10.1137/16M1060741},
}

@incollection {P17,
    AUTHOR = {Pocai, Rafael Veiga},
     TITLE = {Inapproximability ratios for crossing number},
 BOOKTITLE = {L{AGOS}'17---{IX} {L}atin and {A}merican {A}lgorithms,
              {G}raphs and {O}ptimization},
    SERIES = {Electron. Notes Discrete Math.},
    VOLUME = {62},
     PAGES = {117--122},
 PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
      YEAR = {2017},
}

%use BLS19
@ARTICLE{BLS17,
       author = {{Balogh}, J{\'o}zsef and {Lidick{\'y}}, Bernard and {Salazar}, Gelasio},
        title = "{Closing in on Hill's conjecture}",
      journal = {arXiv e-prints},
         year = "2017",
        month = "Nov",
       eprint = {1711.08958},
 primaryClass = {math.CO},
    note = {\arxiv{1711.08958} (last accessed 3/31/2019)},
}

@article {BLS19,
    AUTHOR = {{Balogh}, J{\'o}zsef and {Lidick{\'y}}, Bernard and {Salazar}, Gelasio},
     TITLE = {Closing in on {H}ill's conjecture},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {33},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {1261--1276},
      ISSN = {0895-4801},
   MRCLASS = {05C62 (05C10 68R10)},
  MRNUMBER = {3982073},
MRREVIEWER = {Grant Cairns},
       DOI = {10.1137/17M1158859},
       URL = {https://doi.org/10.1137/17M1158859},
}

@article {BH18,
    AUTHOR = {Burger, Alewyn P. and Harborth, Heiko},
     TITLE = {Numbers of crossings in drawings of the {P}etersen graph},
   JOURNAL = {Geombinatorics},
  FJOURNAL = {Geombinatorics},
    VOLUME = {27},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {97--102},
      ISSN = {1065-7371},
   MRCLASS = {05C62},
  MRNUMBER = {3751972},
}

@article {BFH19,
    AUTHOR = {Burger, Alewyn P. and Feder, Elie and Harborth, Heiko},
     TITLE = {Numbers of crossings for the Cycle graphs},
   JOURNAL = {Geombinatorics},
  FJOURNAL = {Geombinatorics},
    VOLUME = {28},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {158--169},
      ISSN = {1065-7371},
}
	

@article {H16b,
    AUTHOR = {Harborth, Heiko},
     TITLE = {The maximum crossing number of the {P}etersen graph},
   JOURNAL = {Geombinatorics},
  FJOURNAL = {Geombinatorics},
    VOLUME = {26},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {16--22},
      ISSN = {1065-7371},
   MRCLASS = {05C62},
  MRNUMBER = {3585173},
}

%use ACCCHSSTW19
@ARTICLE{ACCCHSSTW18,
   author = {Asplund, John  and Czabarka, {\'{E}}va and Clark, Gregory  and
  Cochran,  Garner  and Hamm, Arran  and Spencer, Gwen  and  Sz{\'e}kely,
              L{\'a}szl{\'o}  and  Taylor, Libby
  and  Wang, Zhiyu},
    title = "{Using Block Designs in Crossing Number Bounds}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1807.03430},
      note = {\arxiv{1807.03430} (last accessed 4/2/2019)},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Discrete Mathematics, 05C10, 57M15},
     year = 2018,
    month = jul,
}


@article {ACCCHSSTW19,
    AUTHOR = {Asplund, John and Clark, Gregory and Cochran, Garner and
              Czabarka, \'{E}va and Hamm, Arran and Spencer, Gwen and Sz\'{e}kely,
              L\'{a}szl\'{o} and Taylor, Libby and Wang, Zhiyu},
     TITLE = {Using block designs in crossing number bounds},
   JOURNAL = {J. Combin. Des.},
  FJOURNAL = {Journal of Combinatorial Designs},
    VOLUME = {27},
      YEAR = {2019},
    NUMBER = {10},
     PAGES = {586--597},
      ISSN = {1063-8539},
   MRCLASS = {05C10 (05B05 05C85 05D40)},
  MRNUMBER = {3998643},
       DOI = {10.1002/jcd.21665},
       URL = {https://doi.org/10.1002/jcd.21665},
}


%use CDKPRW19
@article{CDKPRW18,
  author    = {Steven Chaplick and
               Thomas C. van Dijk and
               Myroslav Kryven and
               Ji{-}won Park and
               Alexander Ravsky and
               Alexander Wolff},
  title     = {Bundled Crossings Revisited},
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2018},
  eprint    = {1812.04263},
  note = {\arxiv{1812.04263} (last accessed 4/2/2019)},
}

@InProceedings{CDKPRW19,
    author="Chaplick, Steven and van Dijk, Thomas C. and Kryven, Myroslav and Park, Ji{-}won and Ravsky, Alexander and Wolff, Alexander",
    editor="Archambault, Daniel and T{\'o}th, Csaba D.",
    title="Bundled Crossings Revisited",
    booktitle="Graph Drawing and Network Visualization",
    year="2019",
    publisher="Springer International Publishing",
    address="Cham",
    pages="63--77",
    isbn="978-3-030-35802-0"
}

@article {Z19,
    AUTHOR = {Zhang, Xin},
     TITLE = {Upper bound on the sum of powers of the degrees of graphs with
              few crossings per edge},
   JOURNAL = {Appl. Math. Comput.},
  FJOURNAL = {Applied Mathematics and Computation},
    VOLUME = {350},
      YEAR = {2019},
     PAGES = {163--169},
      ISSN = {0096-3003},
   MRCLASS = {05C07 (05C10 92E10)},
  MRNUMBER = {3901754},
       DOI = {10.1016/j.amc.2019.01.002},
       URL = {https://doi.org/10.1016/j.amc.2019.01.002},
}


@article{L19,
  author    = {Yoonah Lee},
  title     = {On Genus $g$ Orientable Crossing Numbers of Small Complete Graphs},
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2019},
  eprint    = {1902.02759 },
  note = {\arxiv{1902.02759} (last accessed 4/2/2019)},
}


%don't use, use AFMFHTPVZ19b
@inproceedings{AFMFHTPVZ19,
  author    = {Aichholzer, Oswin  and Fabila-Monroy,  Ruy  and Fuchs, Adrian  and
  Hidalgo-Toscano, Carlos and Parada, Irene  and  Vogtenhuber, Birgit and Zaragoza, Francisco},
  title     = {On the 2-Colored Crossing Number},
  booktitle = {EuroCG 2019},
  year      = {2019},
  note = {\url{http://www.eurocg2019.uu.nl/papers/56.pdf} (last accessed 4/2/2019)},
}

@InProceedings{AFMFHTPVZ19b,
    author="Aichholzer, Oswin and Fabila-Monroy, Ruy and Fuchs, Adrian and Hidalgo-Toscano, Carlos
            and Parada, Irene and Vogtenhuber, Birgit and Zaragoza, Francisco",
    editor="Archambault, Daniel and T{\'o}th, Csaba D.",
    title="On the 2-Colored Crossing Number",
    booktitle="Graph Drawing and Network Visualization",
    year="2019",
    publisher="Springer International Publishing",
    address="Cham",
    pages="87--100",
    isbn="978-3-030-35802-0"
}


@article{CHN19,
  author    = {Clancy, Kieran and Haythorpe, Michael and Newcombe, Alex},
  title     = {A survey of graphs with known or bounded crossing numbers},
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2019},
  eprint    = {1901.05155},
  note = {\arxiv{1901.05155} (last accessed 2/3/2020)},
}



@article {BDGHL18,
    AUTHOR = {Binucci, Carla and Di Giacomo, Emilio and Hossain, Md. Iqbal
              and Liotta, Giuseppe},
     TITLE = {1-page and 2-page drawings with bounded number of crossings
              per edge},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {68},
      YEAR = {2018},
     PAGES = {24--37},
      ISSN = {0195-6698},
   MRCLASS = {05C62 (68R10)},
  MRNUMBER = {3720242},
MRREVIEWER = {Stephen K. Wismath},
       DOI = {10.1016/j.ejc.2017.07.009},
       URL = {https://doi.org/10.1016/j.ejc.2017.07.009},
}
		
@incollection {E17,
    AUTHOR = {Elkies, Noam D.},
     TITLE = {Crossing numbers of complete graphs},
 BOOKTITLE = {The mathematics of various entertaining subjects. {V}ol. 2},
     PAGES = {218--249},
 PUBLISHER = {Princeton Univ. Press, Princeton, NJ},
      YEAR = {2017},
   MRCLASS = {05C62 (05C10 68R10)},
  MRNUMBER = {3701434},
MRREVIEWER = {Robert Cimikowski},
}

@article {BFHHL15,
    AUTHOR = {Bode, Jens-P. and Feder, Elie and Harborth, Heiko and
              Horowitz, David and Lichter, Tamar},
     TITLE = {Extremal values of the maximum rectilinear crossing number of
              {$(p,q)$}-graphs},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {223},
      YEAR = {2015},
     PAGES = {139--149},
      ISSN = {0384-9864},
   MRCLASS = {05C62 (05C35)},
  MRNUMBER = {3468316},
}

%use UW19a
@misc{UW19,
author="Urschel, John C. and Wellens, Jake",
title="Testing $k$-planarity is {NP}-complete",
note={Available at  \url{http://math.mit.edu/~urschel/note.pdf} (last accessed 4/8/2019)}
}


@article{UW19a,
    title={Testing $k$-planarity is {NP}-complete},
    author={John C. Urschel and Jake Wellens},
    journal = {ArXiv e-prints},
    archivePrefix = "arXiv",
    year      = {2019},
    eprint={1907.02104},
    note = {\arxiv{1907.02104} (last accessed 2/10/2020)},
}

@article {FHL17,
    AUTHOR = {Feder, Elie and Harborth, Heiko and Lichter, Tamar},
     TITLE = {Maximum rectilinear crossing numbers of polyomino graphs},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {229},
      YEAR = {2017},
     PAGES = {29--53},
      ISSN = {0384-9864},
   MRCLASS = {05C62},
  MRNUMBER = {3752202},
}


@incollection {FK18,
    AUTHOR = {Fulek, Radoslav and Kyn\v{c}l, Jan},
     TITLE = {The {$\Bbb Z_2$}-genus of {K}uratowski minors},
 BOOKTITLE = {34th {I}nternational {S}ymposium on {C}omputational
              {G}eometry},
    SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
    VOLUME = {99},
     PAGES = {Art. No. 40, 14},
 PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
      YEAR = {2018},
   MRCLASS = {05C10 (05C83)},
  MRNUMBER = {3824284},
}

@article{DFMHVHT19,
  author={Duque, Frank and Fabila-Monroy, Ruy and Hern{\'a}ndez-V{\'e}lez, C{\'e}sar and Hidalgo-Toscano, Carlos},
  title={Counting the Number of Crossings in Geometric Graphs},
  journal = {ArXiv e-prints},
  archivePrefix = "arXiv",
  year      = {2019},
  eprint    = {1904.11037},
  note = {\arxiv{1904.11037} (last accessed 4/30/2019)},
}
}

@incollection{K65,
author = {Koman, Milan},
title = {0 pr\'{a}ci pra\v{z}sk\'{e}ho semin\'{a}\v{r}e teorie graf\r{u}},
booktitle = {V\v{e}deck\'{a} pr\'{a}ce kateder matematiky na Pedagogick\'{y}ch institutech v {\v{C}SSR} },
pages = {89--95},
publisher = {Samostatn\'{a} pedagogick\'{a} fakulta},
address = {Plze\v{n}},
year = 1965,
}


@incollection {BK70,
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     TITLE = {Pr\r{u}se\v{c}\'{\i}kov\'{e} \v{c}\'{\i}slo \'{u}pln\'{y}ch $k$-chromatick\'{y}ch graf\r{u} ({T}he number of intersection points of complete {$k$}-chromatic
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 BOOKTITLE = {Mathematika (geometrie a teorie graf\r{u})},
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 PUBLISHER = {Univ. Karlova, Prague},
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@book{K1669,
  title={Ars magna sciendi, in {XII} libros digesta},
  author={Kircher, Athanasius},
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}

@book{L1517,
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    year = {1517},
    note = {Online at \url{https://archive.org/details/bub_gb_rG_yINh8V1gC} (last accessed 5/17/2019)},
}


%use RR19b
@ARTICLE{RR19,
   author = {Radermacher, Marcel and Rutter, Ignaz},
    title = "{Geometric Crossing-Minimization -- A Scalable Randomized Approach}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
  year      = {2019},
  volume    = {abs/1907.01243},
  url       = {http://arxiv.org/abs/1907.01243},
    note = {\arxiv{1907.01243} (last accessed 7/8/2019)},
}

@incollection {RR19b,
    AUTHOR = {Radermacher, Marcel and Rutter, Ignaz},
     TITLE = {Geometric crossing-minimization---a scalable randomized
              approach},
 BOOKTITLE = {27th {A}nnual {E}uropean {S}ymposium on {A}lgorithms},
    SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
    VOLUME = {144},
     PAGES = {Art. No. 76, 16},
 PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
      YEAR = {2019},
   MRCLASS = {68R10 (60D05 68W20)},
  MRNUMBER = {4007915},
}


@incollection {EdM96,
    AUTHOR = {Eades, P. and de Mendon\c{c}a N., C. F. X.},
     TITLE = {Vertex splitting and tension-free layout},
 BOOKTITLE = {Graph drawing ({P}assau, 1995)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1027},
     PAGES = {202--211},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1996},
   MRCLASS = {68R10 (05C10 05C85 68U05)},
  MRNUMBER = {1400674},
       DOI = {10.1007/BFb0021804},
       URL = {https://doi.org/10.1007/BFb0021804},
}

@article {FdFM01,
    AUTHOR = {Faria, L. and de Figueiredo, C. M. H. and Mendon\c{c}a, C. F. X.},
     TITLE = {S{PLITTING} {NUMBER} is {NP}-complete},
      NOTE = {International Workshop on Graph-Theoretic Concepts in Computer
              Science (Smolenice Castle, 1998)},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {108},
      YEAR = {2001},
    NUMBER = {1-2},
     PAGES = {65--83},
      ISSN = {0166-218X},
   MRCLASS = {05C85 (68Q17 68Q25 68R10)},
  MRNUMBER = {1804713},
MRREVIEWER = {Stanis\l aw P. Radziszowski},
       DOI = {10.1016/S0166-218X(00)00220-1},
       URL = {https://doi.org/10.1016/S0166-218X(00)00220-1},
}


@article{SZ19,
    author={Alireza Shavali and Hamid Zarrabi-Zadeh},
    title={New Bounds on $k$-Planar Crossing Numbers},
    year={2019},
    month=nov,
  journal = {ArXiv e-prints},
    note = {\arxiv{1911.06403} (last accessed 11/21/2019)},
    eprint={1911.06403},
    archivePrefix={arXiv},
    primaryClass={cs.CG}
}

@article{CGN19,
    author = {Cairns, Grant and Groves, Emily and Nikolayevsky, Yuri},
    title = {Bad drawings of small complete graphs},
   JOURNAL = {Australas. J. Combin.},
  FJOURNAL = {The Australasian Journal of Combinatorics},
    VOLUME = {75},
    issue = {3},
      YEAR = {2019},
     PAGES = {322--342},
      ISSN = {2202-3518},
}

@InProceedings{CKMV19,
    author="Chimani, Markus and Kindermann, Philipp and Montecchiani, Fabrizio and Valtr, Pavel",
    editor="Archambault, Daniel and T{\'o}th, Csaba D.",
    title="Crossing Numbers of Beyond-Planar Graphs",
    booktitle="Graph Drawing and Network Visualization",
    year="2019",
    publisher="Springer International Publishing",
    address="Cham",
    pages="78--86",
    isbn="978-3-030-35802-0"
}

@incollection {PSS08d,
    AUTHOR = {Pelsmajer, Michael J. and Schaefer, Marcus and \v{S}tefankovi\v{c},
              Daniel},
     TITLE = {Crossing numbers and parameterized complexity},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4875},
     PAGES = {31--36},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2008},
   MRCLASS = {68Q25 (05C10 68R10)},
  MRNUMBER = {2427804},
       DOI = {10.1007/978-3-540-77537-9_6},
       URL = {https://doi.org/10.1007/978-3-540-77537-9_6},
}


@mastersthesis{M19,
 author = {Musulyan, Marine},
 title = {Local Crossing Numbers of the Product of Planar Graphs and Cycles},
    advisor = "\'{A}brego, Bernardo M. and Rosen, Jerry D. and Fern\'{a}ndez-Merchant, Silvia",
    school ="California State University, Northridge",
    month = "May",
    year = "2019",
    address = "Northridge",
}

@book {S18,
    AUTHOR = {Schaefer, Marcus},
     TITLE = {Crossing numbers of graphs},
    SERIES = {Discrete Mathematics and its Applications (Boca Raton)},
 PUBLISHER = {CRC Press, Boca Raton, FL},
      YEAR = {2018},
     PAGES = {xxvi+350},
      ISBN = {978-1-4987-5049-3},
   MRCLASS = {05-02 (05C10 05C62)},
  MRNUMBER = {3751397},
}
