@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@unpublished{BPR?,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note = "Unpublished manuscript",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},
}

@unpublished{CN?,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}
}

@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},
}

@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} Matousek 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",
}


@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",
}


@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},
}


@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}
}

@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 os},
 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},
year={2013},
issn={0179-5376},
journal={Discrete \& Computational Geometry},
publisher={Springer-Verlag},
pages={1-8},
language={English}
}

@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},
}


@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},
 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},
}



@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},
     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},
    NUMBER = {1},
    PAGES = {\#P1.41},
      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 2013/1/9)},
}

@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},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {6},
      YEAR = {1991},
    NUMBER = {5},
     PAGES = {443--459},
      ISSN = {0179-5376},
}

@article {CK97,
    AUTHOR = {Chrobak, Marek and Kant, Goos},
     TITLE = {Convex grid drawings of {$3$}-connected planar graphs},
   JOURNAL = {Internat. J. Comput. Geom. Appl.},
  FJOURNAL = {International Journal of Computational Geometry \&
              Applications},
    VOLUME = {7},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {211--223},
      ISSN = {0218-1959},
}

@article {K68,
    AUTHOR = {Kainen, Paul C.},
     TITLE = {On a problem of {P}. {E}rd{\H o}s},
   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.},
     TITLE = {On stable crossing numbers},
   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},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {36},
      YEAR = {1972},
     PAGES = {55--62},
      ISSN = {0002-9939},
}

@article {M65,
    AUTHOR = {Moon, J. W.},
     TITLE = {On the distribution of crossings in random complete graphs},
   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},
   JOURNAL = {Mathematika},
  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},
   JOURNAL = {Math. Intelligencer},
  FJOURNAL = {The Mathematical Intelligencer},
    VOLUME = {32},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {41--48},
      ISSN = {0343-6993},
}


@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: December 12th, 2012",
  howpublished = "Available at \url{ftp://ftp.ifi.savba.sk/pub/imrich/crobib.pdf}",

}

@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},
    note = {To appear.}
}

@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,
    AUTHOR = {Verbitsky, Oleg},
     TITLE = {On the obfuscation complexity of planar graphs},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {396},
      YEAR = {2008},
    NUMBER = {1-3},
     PAGES = {294--300},
      ISSN = {0304-3975},
}

@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",
  URL =  	"http://arxiv.org/abs/0803.0858",
}

@article {K70,
    AUTHOR = {Kleitman, Daniel J.},
     TITLE = {The crossing number of {$K_{5,n}$}},
   JOURNAL = {J. Combinatorial Theory},
    VOLUME = {9},
      YEAR = {1970},
     PAGES = {315--323},
}

@article {BD92,
    AUTHOR = {Bienstock, Daniel and Dean, Nathaniel},
     TITLE = {New results on rectilinear crossing numbers and plane
              embeddings},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {16},
      YEAR = {1992},
    NUMBER = {5},
     PAGES = {389--398},
      ISSN = {0364-9024},
}

@article {W93,
    AUTHOR = {Woodall, D. R.},
     TITLE = {Cyclic-order graphs and {Z}arankiewicz's crossing-number
              conjecture},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {17},
      YEAR = {1993},
    NUMBER = {6},
     PAGES = {657--671},
      ISSN = {0364-9024},
}

@book {G72b,
    AUTHOR = {Gr{\"u}nbaum, Branko},
     TITLE = {Arrangements and spreads},
      series = {Conference Board of the Mathematical Sciences Regional
              Conference Series in Mathematics, No. 10},
 PUBLISHER = {American Mathematical Society Providence, R.I.},
      YEAR = {1972},
     PAGES = {iv+114},
}

@book {C1889,
    AUTHOR = {Chrystal, G.},
     TITLE = {Algebra: {A}n elementary text-book for the higher classes of
              secondary schools and for colleges},
     part = {2},
 PUBLISHER = {Adam and Charles Black},
   ADDRESS = {Edinburgh},
      YEAR = {1889},
     PAGES = {xxiv+616},
}

@misc{S04x,
   author = "David Singmaster",
   title = "Sources in Recreational Mathematics. {A}n Annotated Bibliography",
   edition = "8",
   url = "http://www.g4g4.com/MyCD5/SOURCES",
   year = "2004",
}

@article {S69,
    AUTHOR = {Saaty, Thomas L.},
     TITLE = {Symmetry and the crossing number for complete graphs},
   JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
  FJOURNAL = {Journal of Research of the National Bureau of Standards},
    VOLUME = {73B},
      YEAR = {1969},
     PAGES = {177--186},
      ISSN = {0160-1741},
}

@article {S23,
    AUTHOR = {Steinitz, Ernst},
     TITLE = {\"{U}ber die {M}aximalzahl der {D}oppelpunkte bei ebenen
              {P}olygonen von gerader {S}eitenzahl},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {17},
      YEAR = {1923},
    NUMBER = {1},
     PAGES = {116--129},
      ISSN = {0025-5874},
}

@article {AFH09,
    AUTHOR = {Alpert, Matthew and Feder, Elie and Harborth, Heiko},
     TITLE = {The maximum of the maximum rectilinear crossing numbers of
              {$d$}-regular graphs of order {$n$}},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {Research Paper 54},
      ISSN = {1077-8926},
}
		
@article {PRS94,
    AUTHOR = {Piazza, B. L. and Ringeisen, R. D. and Stueckle, S. K.},
     TITLE = {Subthrackleable graphs and four cycles},
      NOTE = {Graph theory and applications (Hakone, 1990)},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {127},
      YEAR = {1994},
    NUMBER = {1-3},
     PAGES = {265--276},
      ISSN = {0012-365X},
}

@inproceedings {GR92,
    AUTHOR = {Green, J. E. and Ringeisen, R. D.},
     TITLE = {Lower bounds for the maximum crossing number using certain
              subgraphs},
 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 = {90},
      YEAR = {1992},
     PAGES = {193--203},
      ISSN = {0384-9864},
}

@article {RSP91,
    AUTHOR = {Ringeisen, R. D. and Stueckle, S. K. and Piazza, B. L.},
     TITLE = {Subgraphs and bounds on maximum crossings},
   JOURNAL = {Bull. Inst. Combin. Appl.},
  FJOURNAL = {Bulletin of the Institute of Combinatorics and its
              Applications},
    VOLUME = {2},
      YEAR = {1991},
     PAGES = {33--46},
      ISSN = {1183-1278},
}

@incollection {PRS91,
    AUTHOR = {Piazza, B. L. and Ringeisen, R. D. and Stueckle, S. K.},
     TITLE = {Properties of nonminimum crossings for some classes of graphs},
 BOOKTITLE = {Graph theory, combinatorics, and applications. {V}ol.\ 2
              ({K}alamazoo, {MI}, 1988)},
    SERIES = {Wiley-Intersci. Publ.},
     PAGES = {975--989},
 PUBLISHER = {Wiley},
   ADDRESS = {New York},
      YEAR = {1991},
}

@article {R96,
    AUTHOR = {Ringeisen, R. D.},
     TITLE = {Two old extremal graph drawing conjectures: progress and
              perspectives},
      NOTE = {Surveys in graph theory (San Francisco, CA, 1995)},
   JOURNAL = {Congr. Numer.},
  FJOURNAL = {Congressus Numerantium. A Conference Journal on Numerical
              Themes},
    VOLUME = {115},
      YEAR = {1996},
     PAGES = {91--103},
      ISSN = {0384-9864},
}

@article {RB78,
    AUTHOR = {Ringeisen, Richard D. and Beineke, Lowell W.},
     TITLE = {The crossing number of {$C_{3}\times C_{n}$}},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {24},
      YEAR = {1978},
    NUMBER = {2},
     PAGES = {134--136},
      ISSN = {0095-8956},
}

@article {BR80,
    AUTHOR = {Beineke, Lowell W. and Ringeisen, Richard D.},
     TITLE = {On the crossing numbers of products of cycles and graphs of
              order four},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {4},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {145--155},
      ISSN = {0364-9024},
}

@incollection {A09,
    AUTHOR = {Archdeacon, Dan},
     TITLE = {Open problems},
 BOOKTITLE = {Topics in topological graph theory},
    SERIES = {Encyclopedia Math. Appl.},
    VOLUME = {128},
     PAGES = {313--336},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2009},
}

@article {H83,
    AUTHOR = {Harary, Frank},
     TITLE = {Maximum versus minimum invariants for graphs},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {7},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {275--284},
      ISSN = {0364-9024},
}

@article {FK76,
    AUTHOR = {Furry, W. H. and Kleitman, D. J.},
     TITLE = {Maximal rectilinear crossing of cycles},
   JOURNAL = {Studies in Appl. Math.},
    VOLUME = {56},
      YEAR = {1976/77},
    NUMBER = {2},
     PAGES = {159--167},
}

@incollection {SSSV95,
    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 = {Book embeddings and crossing numbers},
 BOOKTITLE = {Graph-theoretic concepts in computer science ({H}errsching,
              1994)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {903},
     PAGES = {256--268},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      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.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {155},
      YEAR = {2007},
    NUMBER = {9},
     PAGES = {1106--1115},
      ISSN = {0166-218X},
}

@article {SSSV96,
    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 = {The book crossing number of a graph},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {21},
      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
              in a network},
   JOURNAL = {Proc. Inst. Elec. Engrs.},
  FJOURNAL = {Proceedings of the Institution of Electrical Engineers.
              Electronics. Power. Control \& Science},
    VOLUME = {115},
      YEAR = {1968},
     PAGES = {21--26},
      ISSN = {0020-3270},
}

@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{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},
}

@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},
}

@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,
}

@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, F. and S{\'y}kora, O. and Sz{\'e}kely, L. A. and
              V{\v{r}}{\v{t}}o, I.},
     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",
   eprint = {1105.2723},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics},
     year = 2011,
    month = may,
}

@article {R07,
    AUTHOR = {Riskin, Adrian},
     TITLE = {The circular {$k$}-partite crossing number of {$K_{m,n}$}},
   JOURNAL = {Australas. J. Combin.},
  FJOURNAL = {The Australasian Journal of Combinatorics},
    VOLUME = {38},
      YEAR = {2007},
     PAGES = {207--210},
      ISSN = {1034-4942},
}

@article {R93,
    AUTHOR = {Riskin, Adrian},
     TITLE = {The projective plane crossing number of {$C_3\times C_n$}},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {17},
      YEAR = {1993},
    NUMBER = {6},
     PAGES = {683--693},
      ISSN = {0364-9024},
}

@article {R01,
    AUTHOR = {Riskin, Adrian},
     TITLE = {On the nonembeddability and crossing numbers of some toroidal
              graphs on the {K}lein bottle},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {234},
      YEAR = {2001},
    NUMBER = {1-3},
     PAGES = {77--88},
      ISSN = {0012-365X},
}

@article {JS03,
    AUTHOR = {Juarez, Hector A. and Salazar, Gelasio},
     TITLE = {Optimal meshes of curves in the {K}lein bottle},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {88},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {185--188},
      ISSN = {0095-8956},
}

@ARTICLE{TT10,
   author = "Hiroyuki Tanaka and Masakazu Teragaito",
    title = "{Triple crossing numbers of graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1002.4231},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10},
     year = 2010,
    month = feb,
}

@article {EW94,
    AUTHOR = {Eades, Peter and Wormald, Nicholas C.},
     TITLE = {Edge crossings in drawings of bipartite graphs},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {11},
      YEAR = {1994},
    NUMBER = {4},
     PAGES = {379--403},
      ISSN = {0178-4617},
}

@inproceedings{EMKW86,
  title={On an edge crossing problem},
  author={Eades, Peter and McKay, Brendan D. and Wormald, Nicholas C.},
  booktitle={Proc. 9th Australian Computer Science Conference},
  volume={327},
  pages={334},
  year={1986}
}

@InProceedings{CJS08,
  title =	"Crossing Minimization meets Simultaneous Drawing",
  booktitle={Visualization Symposium, 2008. PacificVIS '08.},
  author =	"Markus Chimani and Michael J{\"u}nger and Michael Schulz",
  publisher =	"IEEE",
  year = 	"2008",
  pages =	"33--40",
}

@incollection {GJPSS06,
    AUTHOR = {Gassner, Elisabeth and J{\"u}nger, Michael and Percan, Merijam
              and Schaefer, Marcus and Schulz, Michael},
     TITLE = {Simultaneous graph embeddings with fixed edges},
 BOOKTITLE = {Graph-theoretic concepts in computer science},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4271},
     PAGES = {325--335},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
}

@article {L00,
    AUTHOR = {Lawrence, J.},
     TITLE = {Mutation polynomials and oriented matroids},
      subtitle = {The Branko Gr{\"u}nbaum birthday issue},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {24},
      YEAR = {2000},
    NUMBER = {2-3},
     PAGES = {365--389},
      ISSN = {0179-5376},
}

@article {CGMW10,
    AUTHOR = {Chimani, Markus and Gutwenger, Carsten and Mutzel, Petra and
              Wong, Hoi-Ming},
     TITLE = {Layer-free upward crossing minimization},
   JOURNAL = {ACM J. Exp. Algorithmics},
  FJOURNAL = {ACM Journal of Experimental Algorithmics},
    VOLUME = {15},
      YEAR = {2010},
     PAGES = {Paper 2.2, 27},
      ISSN = {1084-6654},
}

@article {GT01b,
    AUTHOR = {Garg, Ashim and Tamassia, Roberto},
     TITLE = {On the computational complexity of upward and rectilinear
              planarity testing},
   JOURNAL = {SIAM J. Comput.},
  FJOURNAL = {SIAM Journal on Computing},
    VOLUME = {31},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {601--625},
      ISSN = {0097-5397},
}

@article {N01,
author = {Negami, Seiya},
title = {Crossing numbers of graph embedding pairs on closed surfaces},
journal = {Journal of Graph Theory},
volume = {36},
number = {1},
publisher = {John Wiley & Sons, Inc.},
issn = {1097-0118},
pages = {8--23},
keywords = {crossing numbers, embeddings of graphs},
year = {2001},
}

@article {N98,
    AUTHOR = {Negami, Seiya},
     TITLE = {Diagonal flips in triangulations on closed surfaces,
              estimating upper bounds},
   JOURNAL = {Yokohama Math. J.},
  FJOURNAL = {Yokohama Mathematical Journal},
    VOLUME = {45},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {113--124},
      ISSN = {0044-0523},
}

@article{M85,
 author = {May, Michael},
 title = {Computer-generated multi-row schematics},
 journal = {Comput. Aided Des.},
 volume = {17},
 issue = {1},
 month = {January},
 year = {1985},
 issn = {0010-4485},
 pages = {25--29},
 numpages = {5},
 publisher = {Butterworth-Heinemann},
 address = {Newton, MA, USA},
}

@article {PR04b,
    AUTHOR = {Pinontoan, Benny and Richter, R. Bruce},
     TITLE = {Crossing numbers of sequences of graphs. {I}. {G}eneral tiles},
   JOURNAL = {Australas. J. Combin.},
  FJOURNAL = {The Australasian Journal of Combinatorics},
    VOLUME = {30},
      YEAR = {2004},
     PAGES = {197--206},
      ISSN = {1034-4942},
}

@article {H02,
    AUTHOR = {Harborth, Heiko},
     TITLE = {Special numbers of crossings for complete graphs},
      booktitle = {Algebraic and topological methods in graph theory (Lake Bled,
              1999)},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {244},
      YEAR = {2002},
    NUMBER = {1-3},
     PAGES = {95--102},
      ISSN = {0012-365X},
}


@book {A68,
    AUTHOR = {Atneosen, Gail Adele},
    title = {On the Embeddability of Compacta in {N}-Books: Intrinsic and Extrinsic Properties},
      NOTE = {Thesis (Ph.D.)--Michigan State University},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1968},
     PAGES = {79},
 }

 @book {W84,
    AUTHOR = {White, Arthur T.},
     TITLE = {Graphs, groups and surfaces},
    SERIES = {North-Holland Mathematics Studies},
    VOLUME = {8},
   EDITION = {Second},
 PUBLISHER = {North-Holland Publishing Co.},
   ADDRESS = {Amsterdam},
      YEAR = {1984},
     PAGES = {xiii+314},
}

@InProceedings{M93,
  author =	"Miki Shimabara Miyauchi",
  title =	"Algorithms for Embedding Graphs Into a $3$-Page Book",
  pages =	"79--80",
  booktitle =	"Proc. {ALCOM} Int. Work. Graph Drawing, GD",
  year = 	"1993",
  editor =	"G. {Di Battista} and P. Eades and H. {de} Fraysseix
		 and P. Rosenstiehl and R. Tamassia",
  month =	"26--29~" # sep,
  location =	"S{\`e}vres, France",
  publisher =	"Centre D'Analyse et de Math{\'e}matique Sociales,
		 Paris Sorbonne",
}

@Article{EM99,
  author =	"Hikoe Enomoto and Miki Shimabara Miyauchi",
  title =	"Embedding graphs into a three page book with ${O}(m
		 \log n)$ crossings of edges over the spine",
  journal =	"SIAM J. Disc.~Math.",
  pages =	"337--341",
  year = 	"1999",
  number =	"3",
  volume =	"12",
  editor =	"David B. Shmoys",
  publisher =	"Society for Industrial and Applied Mathematics",
  address =	"Philadelphia, PA",
}

@Article{M05,
  title =	"Embedding a Graph into a $d + 1$-page Book with $\lceil m \log_d n\rceil$ Edge-crossings over the Spine",
  author =	"Miki Miyauchi",
  journal =	"IEICE Transactions",
  year = 	"2005",
  number =	"5",
  volume =	"88-A",
  pages =	"1136--1139",
}

@InProceedings{MS08,
  title =	"Spine Crossing Minimization in Upward Topological Book
		 Embeddings",
  author =	"Tamara Mchedlidze and Antonios Symvonis",
  publisher =	"Springer",
  year = 	"2008",
  volume =	"5417",
  booktitle =	"Graph Drawing",
  editor =	"Ioannis G. Tollis and Maurizio Patrignani",
  ISBN = 	"978-3-642-00218-2",
  pages =	"445--446",
  series =	"Lecture Notes in Computer Science",
}

@InProceedings{BH11,
  title =	"Space crossing numbers",
  author =	"Boris Bukh and Alfredo Hubard",
  booktitle =	"Proceedings of the 27th {ACM} Symposium on
		 Computational Geometry, Paris, France, June 13-15,
		 2011",
  publisher =	"ACM",
  year = 	"2011",
  editor =	"Ferran Hurtado and Marc J. van Kreveld",
  ISBN = 	"978-1-4503-0682-9",
  pages =	"163--170",
}

@book {SU97,
    AUTHOR = {Scheinerman, Edward R. and Ullman, Daniel H.},
     TITLE = {Fractional graph theory},
    SERIES = {Wiley-Interscience Series in Discrete Mathematics and
              Optimization},
 PUBLISHER = {John Wiley \& Sons Inc.},
   ADDRESS = {New York},
      YEAR = {1997},
     PAGES = {xviii+211},
      ISBN = {0-471-17864-0},
}

@article {EGM07,
    AUTHOR = {Eppstein, David and Goodrich, Michael T. and Meng, Jeremy Yu},
     TITLE = {Confluent layered drawings},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {47},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {439--452},
      ISSN = {0178-4617},
}

@Article{HPSS07,
  title =	"Train Tracks and Confluent Drawings",
  author =	"Peter Hui and Michael J. Pelsmajer and Marcus Schaefer
		 and Daniel \v{S}tefankovi\v{c}",
  journal =	"Algorithmica",
  year = 	"2007",
  number =	"4",
  volume =	"47",
  pages =	"465--479",
}

@article {DEGM05,
    AUTHOR = {Dickerson, Matthew and Eppstein, David and Goodrich, Michael
              T. and Meng, Jeremy Y.},
     TITLE = {Confluent drawings: visualizing non-planar diagrams in a
              planar way},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {9},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {31--52},
      ISSN = {1526-1719},
}

@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
              transportation maps},
 BOOKTITLE = {Graph drawing},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4372},
     PAGES = {270--281},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      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},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4875},
     PAGES = {231--242},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2008},
}

@article {ABKS10,
    AUTHOR = {Argyriou, Evmorfia and Bekos, Michael A. and Kaufmann, Michael
              and Symvonis, Antonios},
     TITLE = {On metro-line crossing minimization},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {14},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {75--96},
      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},
    publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-642-18380-5},
  pages = {74-85},
   volume = {6543},
   year = {2011}
}

@article {BBBH11,
    AUTHOR = {Bachmaier, Christian and Brandenburg, Franz J. and Brunner,
              Wolfgang and H{\"u}bner, Ferdinand},
     TITLE = {Global {$k$}-level crossing reduction},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {15},
      YEAR = {2011},
    NUMBER = {5},
     PAGES = {631--659},
      ISSN = {1526-1719},
}

@Article{B07,
  title =	"A Radial Adaptation of the Sugiyama Framework for
		 Visualizing Hierarchical Information",
  author =	"Christian Bachmaier",
  journal =	"IEEE Trans. Vis. Comput. Graph",
  year = 	"2007",
  number =	"3",
  volume =	"13",
  pages =	"583--594",
}

@article {BBF05,
    AUTHOR = {Bachmaier, Christian and Brandenburg, Franz J. and Forster,
              Michael},
     TITLE = {Radial level planarity testing and embedding in linear time},
   JOURNAL = {J. Graph Algorithms Appl.},
  FJOURNAL = {Journal of Graph Algorithms and Applications},
    VOLUME = {9},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {53--97},
      ISSN = {1526-1719},
}

@incollection {MZ99,
    AUTHOR = {Mutzel, Petra and Ziegler, Thomas},
     TITLE = {The constrained crossing minimization problem---a first
              approach},
 BOOKTITLE = {Operations {R}esearch {P}roceedings 1998 ({Z}urich)},
     PAGES = {125--134},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1999},
}

@incollection {MZ99b,
    AUTHOR = {Mutzel, Petra and Ziegler, Thomas},
     TITLE = {The constrained crossing minimization problem},
 BOOKTITLE = {Graph drawing (\v {S}ti\v r\'\i n {C}astle, 1999)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1731},
     PAGES = {175--185},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1999},
}

@article {DEKW06,
    AUTHOR = {Duncan, Christian A. and Efrat, Alon and Kobourov, Stephen and
              Wenk, Carola},
     TITLE = {Drawing with fat edges},
   JOURNAL = {Internat. J. Found. Comput. Sci.},
  FJOURNAL = {International Journal of Foundations of Computer Science},
    VOLUME = {17},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {1143--1163},
      ISSN = {0129-0541},
}

@article {DV12,
   author = {Djidjev, Hristo and  V{\v{r}}{\v{t}}o, Imrich},
   affiliation = {Los Alamos National Laboratory, Los Alamos, NM 87544, USA},
   title = {Planar Crossing Numbers of Graphs of Bounded Genus},
   journal = {Discrete \& Computational Geometry},
   publisher = {Springer New York},
   issn = {0179-5376},
   keyword = {Mathematics and Statistics},
   pages = {1-23},
   year = {2012},
}

@mastersthesis{MC12,
 author = {McConvey, Andrew},
 title = {Highly Non-Convex Crossing Sequences},
    advisor = "Richater, Bruce and Salazar, Gelasio",
    school ="University of Waterloo",
    year = "2012",
    address = "Waterloo",
}



@incollection {CM10,
    AUTHOR = {Cabello, Sergio and Mohar, Bojan},
     TITLE = {Adding one edge to planar graphs makes crossing number hard},
 BOOKTITLE = {Computational geometry ({SCG}'10)},
     PAGES = {68--76},
 PUBLISHER = {ACM},
   ADDRESS = {New York},
      YEAR = {2010},
}

@article {CM11,
    AUTHOR = {Cabello, Sergio and Mohar, Bojan},
     TITLE = {Crossing number and weighted crossing number of near-planar
              graphs},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {60},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {484--504},
      ISSN = {0178-4617},
}

@incollection {DMS08,
    AUTHOR = {DeVos, Matt and Mohar, Bojan and {\v{S}}{\'a}mal, Robert},
     TITLE = {Unexpected behaviour of crossing sequences},
 BOOKTITLE = {The {I}nternational {C}onference on {T}opological and
              {G}eometric {G}raph {T}heory},
    SERIES = {Electron. Notes Discrete Math.},
    VOLUME = {31},
     PAGES = {259--264},
 PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
      YEAR = {2008},
}

@article {AB01,
    AUTHOR = {Archdeacon, Dan and Bonnington, C. Paul},
     TITLE = {Two maps on one surface},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {36},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {198--216},
      ISSN = {0364-9024},
}

@article {RS05,
    AUTHOR = {Richter, R. Bruce and Salazar, Gelasio},
     TITLE = {Two maps with large representativity on one surface},
   JOURNAL = {J. Graph Theory},
  FJOURNAL = {Journal of Graph Theory},
    VOLUME = {50},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {234--245},
      ISSN = {0364-9024},
     CODEN = {JGTHDO},
}

@misc{H98w,
 author = "Steve Hedetniemi",
 title = "OPEN PROBLEMS IN COMBINATORIAL OPTIMIZATION",
 howpublished = {\url{http://www.cs.clemson.edu/~hedet/algorithms.html} (last accessed 2013/1/9)},
}

@phdthesis{E73,
    author = "Eggleton, Roger B.",
    title = "Crossing Numbers of graphs",
    advisor = "Guy, Richard K.",
    school ="University of Calgary",
    year = "1973",
    address = "Calgary",
}

@incollection {G71b,
    AUTHOR = {Guy, Richard K.},
     TITLE = {Latest results on crossing numbers},
 BOOKTITLE = {Recent {T}rends in {G}raph {T}heory ({P}roc. {C}onf., {N}ew
              {Y}ork, 1970)},
     PAGES = {143--156},
 PUBLISHER = {Lecture Notes in Mathematics, Vol. 186. Springer, Berlin},
      YEAR = {1971},
}

@article {K91,
    AUTHOR = {Kratochv{\'{\i}}l, Jan},
     TITLE = {String graphs. {I}. {T}he number of critical nonstring graphs
              is infinite},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {52},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {53--66},
      ISSN = {0095-8956},
}

@Article{K91b,
   AUTHOR = {Kratochv{\'{\i}}l, Jan},
     TITLE = {String graphs. {II}. {R}ecognizing string graphs is {NP}-hard},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {52},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {67--78},
      ISSN = {0095-8956},
       URL = {http://dx.doi.org/10.1016/0095-8956(91)90091-W},
}

@book {D59,
    AUTHOR = {Dudeney, Henry Ernest},
     TITLE = {Amusements in mathematics},
 PUBLISHER = {Dover Publications Inc.},
   ADDRESS = {New York},
      YEAR = {1959},
     PAGES = {xii+258},
}

@inproceedings{KM09,
author = {Vladimir P. Korzhik and Bojan Mohar},
title = {Minimal Obstructions for 1-Immersions and Hardness of 1-Planarity Testing},
  editor    = {Ioannis G. Tollis and
               Maurizio Patrignani},
  booktitle     = {Graph Drawing, 16th International Symposium, GD 2008, Heraklion,
               Crete, Greece, September 21-24, 2008. Revised Papers},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {5417},
  year      = {2009},
  pages     = {302-312},
}

@article {S86,
    AUTHOR = {Schumacher, H.},
     TITLE = {Zur {S}truktur {$1$}-planarer {G}raphen},
   JOURNAL = {Math. Nachr.},
  FJOURNAL = {Mathematische Nachrichten},
    VOLUME = {125},
      YEAR = {1986},
     PAGES = {291--300},
      ISSN = {0025-584X},
}

@article {BSW83,
    AUTHOR = {Bodendiek, R. and Schumacher, H. and Wagner, K.},
     TITLE = {Bemerkungen zu einem {S}echsfarbenproblem von {G}. {R}ingel},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"at
              Hamburg},
    VOLUME = {53},
      YEAR = {1983},
     PAGES = {41--52},
      ISSN = {0025-5858},
}

@InProceedings{G89,
  title =	"On Global Wire Ordering for Macro-Cell Routing",
  author =	"Patrick Groenveld",
  year = 	"1989",
  booktitle =	"26th Conference on Design Automation Conference",
  pages =	"155--160",
  publisher = "IEEE",
  issn = "0738-100X",
}

@Article{CL98,
  title =	"On crossing minimization problem",
  author =	"Hsiao-Feng Steven Chen and D. T. Lee",
  journal =	"IEEE Trans. on CAD of Integrated Circuits and
		 Systems",
  year = 	"1998",
  number =	"5",
  volume =	"17",
  pages =	"406--418",
}

@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},
     TITLE = {On the complexity of crossings in permutations},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    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",
}


@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},
      YEAR = {2010},
     PAGES = {xvi+934},
      ISBN = {978-1-58488-820-8},
}

@book {A06,
    AUTHOR = {Ashlock, Daniel},
     TITLE = {Evolutionary computation for modeling and optimization},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2006},
     PAGES = {xx+571},
      ISBN = {978-0387-22196-0; 0-387-22196-4},
}

@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},
 primaryClass = "math.CO",
     year = 2011,
    month = nov,
}

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

@article{U55,
    author = {Urbanik, K.},
    title = {Solution du probl\`{e}me pos\'{e} par {P}. {T}ur\'{a}n},
    journal = {Comptes Rendus},
    publisher = {Soci\'{e}t\'{e} Polonaise de Math\'{e}mathique},
    year = {1955},
    pages = {200--201},
}

@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},
    VOLUME = {206},
      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},
   JOURNAL = {J. Combin. Theory Ser. A},
  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 {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},
}

@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},
}

@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},
}

@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},
 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
}

@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},
}

@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}
}

@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},
}

@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 2013/1/9)",
 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},
}

@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, Halin
		 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",
}

@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},
}

@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}},
}

@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-Phyische Classe.",
volume = {37},
pages = {1--6},
publisher = {S. Hirzel},
address = {Leipzig},
year = {1884},
}

@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},
}

@ARTICLE{C12,
   author = {Cabello, Sergio},
    title = "{Hardness of approximation for crossing number}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1204.0660},
 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},
 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},
}

@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},
}

@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 1/12/2013)},
}

%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},
}

@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},
 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="CycleXings",
  note = "Game presented at {\em Graph Drawing '12}",
  howpublished = {\url{http://i11www.iti.uni-karlsruhe.de/projects/cyclexings/index} (last accessed 2013/1/9)},
  year = "2012",
}

@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},
 primaryClass = "math.CO",
     year = 2012,
    month = oct,

}

@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",
}

@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 2013/1/9))},
 year = {2012},
}
 
@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 (\url{http://www.math.illinois.edu/REGS/reports12/Erickson-Kim-Wang-Yeager.pdf}, last accessed 2013/1/9)},
 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},
}

@ARTICLE{M13,
   author = {{Matousek}, Ji\v{r}\'{\i}},
    title = "{Near-optimal separators in string graphs}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1302.6482},
 primaryClass = "math.CO",
     year = 2013,
    month = feb,
}

@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},
     year = 2013,
    month = mar,
}

@misc{E13,
 author = "David Eppstein",
 title = "An early reference on crossing minimization",
 howpublished = {\url{http://11011110.livejournal.com/265544.html} (last accessed 2013/4/1)},
}

@misc{E13a,
 author = "David Eppstein",
 title = "A Brief History of Curves in Graph Drawing",
 howpublished = {\url{http://11011110.livejournal.com/266622.html} (last accessed 2013/4/9)},
}

@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},
}

@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},
     year = 2013,
    month = apr,
}


@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},
     year = 2013,
    month = apr,
}

@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},
     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}
}

@ARTICLE{FP13,
   author = {{Fink}, Martin and {Pupyrev}, Sergey},
    title = "{Ordering Metro Lines by Block Crossings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1305.0069},
 primaryClass = "cs.DS",
     year = 2013,
    month = apr,
}


@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},
 primaryClass = "cs.DS",
     year = 2013,
    month = jun,
}

@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},
 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 = {T{HE} {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. and Jenkyns, T. A.},
    TITLE = {The planad 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/chromovisGD2013.pdf} (last accessed 7/9/2013)},
 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, J. and Koman, M.},
     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 {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},
}

@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},
 primaryClass = "cs.CG",
 keywords = {Computer Science - Computational Geometry},
     year = 2013,
    month = aug,
}



@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},
}

@unpublished{GMS1?,
 author = {Gutwenger, Carsten and Mutzel, Petra and Schaefer, Marcus},
 title = {Practical Experience with Hanani-Tutte for Testing $c$-Planarity},
 note = {To be presented at ALENEX 2014.},
}

@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},
 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",
   url = "\url{http://en.wikipedia.org/wiki/Existential_theory_of_the_reals}",
   note = "(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},
}

@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},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics},
     year = 2013,
    month = sep,
}

@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},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, Computer Science - Computational Geometry, 05C10, 05C62, 52C10},
     year = 2013,
    month = sep,
}

@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},
     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},
}

@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},
 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{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}
}

@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},
     year = 2013,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1311.1994Z},
}
@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}
}

@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},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10},
     year = 2013,
    month = dec,
   adsurl = {http://adsabs.harvard.edu/abs/2013arXiv1312.3679B},
}

@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},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 05C62, 05C83, 05C85, 57M15, 68R10},
     year = 2014,
    month = mar,
}

@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},
}

@inbook{GMS14,
author = {Gutwenger, Carsten and Mutzel, Petra and Schaefer, Marcus},
title = {Practical Experience with Hanani-Tutte for Testing $c$-Planarity},
booktitle = {2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX)},
chapter = {8},
pages = {86-97},
doi = {10.1137/1.9781611973198.9},
URL = {http://epubs.siam.org/doi/abs/10.1137/1.9781611973198.9},
eprint = {http://epubs.siam.org/doi/pdf/10.1137/1.9781611973198.9}
}

@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{FML14,
   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},
 primaryClass = "math.CO",
     year = 2014,
    month = mar,
 }
 
@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}
}

@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)},
}


@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},
 primaryClass = "math.CO",
 keywords = {Mathematics - Combinatorics, 05C10, 52C30, 68R10, 05C62},
     year = 2014,
    month = apr,
}

@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},
}
