Venn Diagram Survey

References to Venn Diagrams

  1. [AC] Daniel E. Anderson and Frank L. Cleaver, Venn-type diagrams for arguments of n terms, J. Symbolic Logic, 30 (1965) 113-118.
  2. [An] J. Anusiak, On Set-theoretically Independent Collections of Balls, Colloquium Mathematicum, 13 (1965) 223-233.
  3. [Baker] M.J.C. Baker, All swans are white: some remarks on the diagrams of Euler and Venn, Australian Math. Soc. Gaz., 17 (1990) 161-167. (MR 91k:04007)
  4. [Ba] Margaret E. Baron, A Note on the historical development of logic diagrams: Leibniz, Euler, and Venn, Mathematical Gazette, 52 (1969) 113-125.
  5. [Be] E.C. Berkeley, Boolean algebra (the technique for manipulating "and", "or", "not" and conditions) and applications to insurance, The Record, American Institute of Actuaries, 26 (1937) 373-414. [According to [Grün75], this paper contains a general Venn diagram construction].
  6. [Boy] A.V. Boyd, Venn diagram of rectangles, Mathematics Magazine, 58 (1985) 251.
  7. [Bow] L.J. Bowles, Logic diagrams for up to n classes, Mathematical Gazette, 55 (1971) 370-373.
  8. [BuRu] Bette Bultena and Frank Ruskey, Monotone Venn Diagrams with Few Vertices Electronic Journal of Combinatorics, Volume 5, paper R44, 21 pages, 1998.
  9. [BGR]Bette Bultena, Branko Grünbaum, and Frank Ruskey, Convex Drawings of Intersecting Families of Simple Closed Curves, 11th Canadian Conference on Computational Geometry, 1999, 18-21.
  10. [Ca99] J. Carroll, Personal communication, December 1999.
  11. [CHP95] K.B. Chilakamarri, P. Hamburger, and R.E. Pippert, Venn diagrams: announcement of some new results, Geombinatorics, 4 (1995) 129-137.
  12. [CHP96] K.B. Chilakamarri, P. Hamburger, and R.E. Pippert, Hamilton Cycles in Planar Graphs and Venn Diagrams, Journal of Combinatorial Theory (Series B), 67 (1996) 296-303.
  13. [CHP97a] Kiran B. Chilakamarri, Peter Hamburger and Raymond E. Pippert, Simple, reducible Venn diagrams on five curves and Hamiltonian cycles, Geometriae Dedicata, 68 (1997) 245-262.
  14. [CHP96b] Kiran B. Chilakamarri, Peter Hamburger and Raymond E. Pippert, Venn diagrams and planar graphs, Geometriae Dedicata, 62 (1996) 73-91. (MR 98h:05064)
  15. [CHP96b] Kiran B. Chilakamarri, Peter Hamburger and Raymond E. Pippert, Analysis of Venn diagrams using cycles in graphs, Geometriae Dedicata, 82 (2000) 193-223.
  16. [Ed89a] Anthony W. F. Edwards, Venn diagrams for many sets, Bulletin of the International Statistical Institute, 47th Session, Paris, 1989. Contributed papers, Book 1, 311-312.
  17. [Ed89b] Anthony W. F. Edwards, Venn diagrams for many sets, New Scientist, 7 January 1989, 51-56.
  18. [Ed92] Anthony W. F. Edwards, Rotatable Venn Diagrams, Mathematics Review, 2 (February 1992) 19-21.
  19. [Ed96] Anthony W. F. Edwards, Seven-set Venn diagrams with rotational and polar symmetry, Combinatorics, Probability, and Computing, 7 (1998) 149-152.
  20. [ES] Anthony W. F. Edwards and C.A.B. Smith, New 3-set Venn diagram, Nature, (Scientific Correspondence), 339 (1989) 263.
  21. [FKG] J. Chris Fisher, E. L. Koh, and Branko Grünbaum, Diagrams Venn and How, Mathematics Magazine, 61 (1988) 36-40.
  22. [Ga] Martin Gardner, Logic, Machines, and Diagrams, McGraw-Hill, New York, 1958.
  23. [GKP] Ronald Graham, Donald Knuth, and Oren Patashnik, Concrete Mathematics, Addison-Wesley, 1989. [Exercises about Venn diagrams (1.5 and 1.22) may be found on pages 17 and 20, with corresponding solutions on pages 483 and 486.]
  24. [Gr75] Branko Grünbaum, Venn diagrams and Independent Families of Sets, Mathematics Magazine, 48 (Jan-Feb 1975) 12-23. [Grünbaum awarded the MAA Lester R. Ford prize for this paper in 1976 (see AMM, Aug-Sept. 1976, pg. 587).]
  25. [Gr84a] Branko Grünbaum, The Construction of Venn Diagrams, The College Mathematics Journal, 15 (1984) 238-247.
  26. [Gr84b] Branko Grünbaum, On Venn Diagrams and the Counting of Regions, The College Mathematics Journal, 15 (1984) 433-435.
  27. [Gr92a] Branko Grünbaum, Venn Diagrams I, Geombinatorics, Volume I, Issue 4, (1992) 5-12.
  28. [Gr92b] Branko Grünbaum, Venn Diagrams II, Geombinatorics, Volume II, Issue 2, (1992) 25-32.
  29. [Gr99] Branko Grünbaum, The Search for Symmetric Venn Diagrams, Geombinatorics, 8 (1999) 104-109.
  30. [GW] Branko Grünbaum and Peter Winkler, A Venn Diagram of 5 Triangles, Mathematics Magazine, 55 (1982) 311.
  31. [GLT] A. Gyárfás, J. Lehel, and Zs. Tuza, The structure of rectangle families dividing the plane into maximum number of atoms, Discrete Math. 52 (1984) 177-198. (MR 86g:05025)
  32. [Ha98] Peter Hamburger, A Graph-Theoretic Approach to Geometry, manuscript.
  33. [Ha01] Peter Hamburger, Doodles and Doilies, manuscript, 2000.
  34. [HP96a] P. Hamburger and R.E. Pippert, Venn said it couldn't be done, American Scientist, 1996, to appear.
  35. [HP96c] P. Hamburger and R.E. Pippert, Simple, reducible Venn diagrams on five curves and Hamiltonian cycles, Geometriae Dedicata, 1996, to appear.
  36. [He] D. W. Henderson, Venn diagrams for more than four classes, American Mathematical Monthly, 70 (1963) 424-426.
  37. [JP] D.S. Johnson and H.O. Pollack, Hypergraph Planarity and the Complexity of Drawing Venn Diagrams, Journal of Graph Theory, 11 (1987). [Earlier version appears in Colloquim on the Theory of Algorithms, North-Holland, 1985.]
  38. [LL] D.K.J. Lin and A.W. Lam, Connections Between Two-Level Factorials and Venn Diagrams , The American Statistician, 51 (1997) 49-51.
  39. [Mo] T. Moor, Jr. On the construction of Venn diagrams, J. Symbolic Logic, 24 (1959) 303-304.
  40. [No] P. Nowicki, Koniczynko n-listna, [In Polish], Wiadom. Mat., 19 (1975) 11-18.
  41. [Pa] Lewis Pakula, A note on Venn diagrams American Mathematical Monthly, 96 (1989) 38-39. (MR 89k:51040)
  42. [RRS] A. Rényi, V. Rényi, and J. Surányi, Sur l'indépendance des Domaines Simples dans l'espace Euclidien a n dimensions, Colloquium Mathematicum, 2 (1951) 130-135. [Some erroneous statements made in this paper are corrected in [Gr75]]
  43. [Sc] A. J. Schwenk, Venn diagram for five sets, Mathematics Magazine, 57 (1984) 297.
  44. [Shin] Sun-Joo Shin, The logical status of diagrams, Cambridge University Press, 1994. (MR 95j:03014)
  45. [Ve80] J. Venn, On the diagrammatic and mechanical representation of propositions and reasonings, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 9 (1880) 1-18.
  46. [Ve81] J. Venn, Symbolic Logic, MacMillan, London 1881, 2nd ed., 1894.
  47. [We] B. Weglorz, Nerves and Set-theoretical Independence, Colloquium Mathimaticum, 13 (1964) 17-19.
  48. [Wi] Peter Winkler, Venn diagrams: Some observations and an open problem, Congressus Numerantium, 45 (1984) 267-274.
  49. Obscure references (and not necessarily relevant).

    Other References Used

  50. [BS] G.S. Bhat and C.D.Savage, Balanced Gray Codes, Electronic Journal of Combinatorics, Volume 3 (no. 1), #R25 .
  51. [HPB] A.P. Hiltgen and K.G. Paterson, and M. Brandestini, Single-Track Gray Codes, IEEE Trans. Information Theory, 42 (1996) 1555-1561.
  52. [NW] A. Nijenhuis and H.S. Wilf, Combinatorial Algorithms, 2nd. ed., Academic Press, New York, London, 1978.
  53. [Or] O. Ore, The Four-Color Problem, Academic Press, New York, London, 1967.
  54. [St] Ian Stewart, Game, Set, and Math, Basil Blackwell, 1989.
  55. [Wh] H. Whitney, A Theorem on Graphs, Annals of Math., 32 (1931) 378-390.

    Off-site references

    The external sites listed below are not endorsed by The Electronic Journal of Combinatorics and do not form part of this article.

  56. [FAQ] Frank Ruskey maintains a small FAQ (frequently asked questions) containing the answers to some questions he received about Venn diagrams, but are outside the scope of this survey.
  57. [COS] The set partitions information page, part of the Combinatorial Object Server.
  58. [JC] Jeremy Carroll's page about his solution of the 6-Venn triangle problem. Make sure that you try out his Java applet!
  59. [SJ] Slavik Jablan's page "Are Borromean Links so Rare?"
  60. [PH] Peter Hamburger's paper about his solution to the symmetric 11-Venn diagram problem, entitled Doodles and Doilies
  61. [MAC] The MacTutor History of Mathematics Archive contains a short biography of John Venn.
  62. [GC] The Geometry Center at the University of Minnesota.
  63. [KP] Robert Scharein's KnotPlot site. All pictures of knots on this site were produced with KnotPlot.