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Four Color Theorem (4CT) – Resources

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  1. Aigner, M. (1984). Graphentheorie: eine Entwicklung aus dem 4-Farben Problem. Stuttgart: B.G. Teubner. Library Catalog Record
  2. Aigner, M. (1987). Graph theory: a development from the 4-color problem. Moscow, ID: BCS Associates. Library Catalog Record
  3. Allaire, F. (1978). Another proof of the four colour theorem. I. In Proceedings of the Seventh Manitoba Conference on Numerical Mathematics and Computing (pp. 3–72).Winnipeg: Utilitas Mathematica Publishing. Library Catalog Record
  4. Appel, K., & Haken, W. (1976). Every planar map is four colorable. Bulletin of the American Mathematical Society, 82(5), 711–712. Full-text available online (subscription required).
  5. Appel, K., & Haken, W. (1976). Every planar map is four colorable. Journal of Recreational Mathematics, 9(3), 161. Library Catalog Record
  6. Appel, K., & Haken, W. (1976). Special announcement: A proof of the four color theorem. Discrete Mathematics, 16(2), 179–180. Full-text available online (subscription required).
  7. Appel, K., & Haken, W. (1976). The existence of unavoidable sets of geographically good configurations. Illinois Journal of Mathematics, 20(2), 218–297. Full-text available online (subscription required).
  8. Appel, K., & Haken, W. (1977). Every planar map is four colorable. Part I: Discharging. Illinois Journal of Mathematics, 21(3), 429–490. Full-text available online (subscription required).
  9. Appel, K, & Haken, W. (1979). An unavoidable set of configurations in planar triangulations. Journal of Combinatorial Theory, Series B, 26(1), 1–21. Full-text available online (subscription required).
  10. Appel, K., & Haken, W. (1986). The four color proof suffices. The Mathematical Intelligencer, 8(1), 10–20.  Full-text available online (subscription required).
  11. Appel, K., & Haken, W. (1989). Every Planar Map is Four Colorable. American Mathematical Society, 98. Full-text available online (subscription required).
  12. Appel, K., Haken, W., & Koch, J. (1977). Every planar map is four colorable. Part II: Reducibility. Illinois Journal of Mathematics, 21(3), 491–567. Full-text available online (subscription required).
  13. Ball, W. W. R., & Coxeter, H. S. M. (1987). Map-colouring problems. In W. W. R. Ball & H. S. M. Coxeter, Mathematical recreations and essays (13th ed., p. 222). New York: Dover Publications. Library Catalog Record
  14. Bar-Natan, D. (1997). Lie algebras and the Four Color Theorem. Combinatorica, 17(1), 43–52.  Full-text available online (subscription required).
  15. Bernhart, F. R. (1977). A digest of the four color theorem. Journal of Graph Theory, 1(3), 207-225. Full-text available online (subscription required).
  16. Biggs, N. L. (1983). De morgan on map colouring and the separation axiom. Archive for History of Exact Sciences, 28(2), 165–170. Full-text available online (subscription required).
  17. Biggs, N. L., Lloyd, E. K., & Wilson, R. J. (1976). Graph theory: 1736–1936. Oxford: Clarendon Press. Library Catalog Record
  18. Birkhoff, G. D. (1913). The Reducibility of Maps. American Journal of Mathematics, 35(2), 115–128. Full-text available online (subscription required).
  19. Burger, E. B., & Morgan, F. (1997). Fermat’s Last Theorem, the Four Color Conjecture, and Bill Clinton for April Fools’ Day. The American Mathematical Monthly, 104(3), 246–255. Full-text available online (subscription required).
  20. Chartrand, G., & Lesniak, L. (2005). Graphs & digraphs (4th ed.). Boca Raton: Chapman & Hall/CRC. Library Catalog Record
  21. Dailey, D. P. (1980). Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete. Discrete Mathematics, 30(3), 289–293.  Full-text available online (subscription required).
  22. Dirac, G. A., & Stojaković, M. D. (1960). Problem četiri boje (Vol. 16). Beograd: Katedra za matematiku Elektrotehničkog fakulteta univerziteta u Beogradu. Library Catalog Record
  23. Dowek, G., Guillot, P., & Roman, M. (2015). Computation, proof, machine: Mathematics enters a new age (1st ed.). New York, NY: Cambridge University Press. Full-text available online (subscription required).
  24. Dynkin, E. B., & Uspenski, W. A. (1979). Mathematische Unterhaltungen: Aufgaben über das Mehrfarbenproblem, aus der Zahlentheorie und der Wahrscheinlichkeitsrechnung. Köln: Aulis Verlag Deubner. Library Catalog Record
  25. Errera, A. (1927). Exposé historique du problème des quatre couleurs. Periodico di Matematiche. IV. Serie, 7, 20–41. Library Catalog Record
  26. Fritsch, R. (1994). Der Vierfarbensatz: Geschichte, topologische Grundlagen, und Beweisidee. Mannheim: B.I.-Wissenschaftsverlag. Library Catalog Record
  27. Fritsch, R., & Fritsch, G. (1998). The Four-Color Theorem: History, Topological Foundations, and Idea of Proof. New York, NY: Springer New York. Full-text available online (subscription required).
  28. Gonthier, G. (2008). Formal Proof – The Four-Color Theorem. Notices of the American Mathematical Society, 55(11), 1382–1393. Full-text available online (subscription required).
  29. Guthrie, F. (1880). 9. Note on the Colouring of Maps. In Proceedings of the Royal Society of Edinburgh, 10, 727–728. Full-text available online (subscription required).
  30. Hadwiger, H. (1943). Über eine Klassifickation der Strekenkomplexe. In Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich (Vol. 88). Zürich: Fäsi & Beer. Library Catalog Record
  31. Haken, W. (1977). An attempt to understand the four color problem. Journal of Graph Theory, 1(3), 193-206. Full-text available online (subscription required).
  32. Haken, W. (1980). Combinatorial aspects of some mathematical problems. In Proceedings of the International Congress of Mathematicians (pp. 953–961). Toronto: University of Toronto Press. Library Catalog Record
  33. Heawood, P. J. (1890). Map-colour theorem. The Quarterly Journal of Pure and Applied Mathematics, 24, 332–338. Library Catalog Record
  34. Heawood, P. J. (1949). Map-colour theorem. Proceedings of the London Mathematical Society, 2(51), 161-175. Full-text available online (subscription required).
  35. Heesch, H. (1969). Untersuchungen zum Vierfarbenproblem (Vol. 810). Mannheim: Bibliographisches Institut. Library Catalog Record
  36. Hitotsumatsu, S. (1978). Shishiki mondai: sono tanjō kara kaiketsu made. Tōkyō: Kōdansha, cShōwa 53. Library Catalog Record
  37. Hudson, H. (2003). Four Colors Do Not Suffice. The American Mathematical Monthly, 110(5), 417–423. Full-text available online (subscription required).
  38. Kauffman, L. H. (1994). Spin networks, topology and discrete physics. In Yang, C. N., & Ge, M. L. (Eds.), Braid group, knot theory and statistical mechanics. II (Vol. 17, pp. 234–274). River Edge, NJ: World Scientific Publishing Co., Inc.  Library Catalog Record
  39. Koch, J. A. (1976). Computation of four color irreducibility. Urbana: Department of Computer Science, University of Illinois at Urbana-Champaign. Full-text available online (subscription required).
  40. May, K. O. (1965). The Origin of the Four-Color Conjecture. Isis, 56(3), 346–348. Full-text available online (subscription required).
  41. Mayer, J. (1974). Nouvelles réductions dans le problème des quatre couleurs. Montpellier: Université des sciences et techniques du Languedoc, U. E. R. de mathématiques. Library Catalog Record
  42. Nash-Williams, C. S. J. A. (1967). Infinite graphs – A survey. Journal of Combinatorial Theory, 3(3), 286–301.  Full-text available online (subscription required).
  43. Nelson, R., & Wilson, R. (1990). Graph colourings. Essex, England: Longman. Library Catalog Record
  44. Ore, Ø. (1967). The four-color problem. New York-London: Academic Press. Full-text available online (subscription required). 
  45. Osgood, T. W. (1973). An Existence Theorem for Planar Triangulations With Vertices of Degree Five, Six, and Eight. University of Illinois at Urbana-Champaign. Full-text available online (subscription required).
  46. Robertson, N., Sanders, D., Seymour, P., & Thomas, R. (1997). The Four-Colour Theorem. Journal of Combinatorial Theory, Series B, 70(1), 2–44.  Full-text available online (subscription required).
  47. Saaty, T. L., & Kainen, P. C. (1986). The four-color problem: assaults and conquest. New York : Dover Publications. Library Catalog Record
  48. Stewart, I. (2013). Visions of Infinity: The Great Mathematical Problems. New York, NY: Basic Books. Library Catalog Record
  49. Swart, E. R. (1980). The Philosophical Implications of the Four-Color Problem. The American Mathematical Monthly, 87(9), 697–707. Full-text available online (subscription required).
  50. Tait. (1880). 4. On the Colouring of Maps. In Proceedings of the Royal Society of Edinburgh, 10, 501–503. Full-text available online (subscription required).
  51. Tait. (1880). 10. Remarks on the previous Communication. In Proceedings of the Royal Society of Edinburgh, 10, 729–729. Full-text available online (subscription required).
  52. Thomas, J. M. (1971). The four color theorem (Rev. ed.). Philadelphia. Library Catalog Record
  53. Thomas, J. M. (1977). The four color theorem (Final ed.). Durham, N.C. Library Catalog Record
  54. Thomas, R. (1998). An Update on the Four-Color Theorem. Notices of the American Mathematical Society, 45(7), 848-859. Full-text available online (subscription required).
  55. Thomas, R. (1999). Recent excluded minor theorems for graphs. In J. D. Lamb, & D. A. Preece (Eds.), Surveys in combinatorics, 1999 (Vol. 267, pp. 201–222). New York: Cambridge University Press. Library Catalog Record
  56. Wernicke, P. (1904). Über den kartographischen Vierfarbensatz. Mathematische Annalen, 58(3), 413–426. Full-text available online (subscription required).
  57. Wilson, J. (1976). New light on the origin of the four-color conjecture. Historia Mathematica, 3(3), 329–330. Full-text available online (subscription required).
  58. Wilson, R. A. (2002). Graphs, colourings and the four-colour theorem. Oxford: Oxford University Press. Library Catalog Record
  59. Wilson, R. J. (2002). Four colours suffice: how the map problem was solved. Princeton, NJ: Princeton University Press. Library Catalog Record
  60. Wilson, R. J. (2014). Four colours suffice: how the map problem was solved. Princeton, NJ: Princeton University Press. Library Catalog Record

Additional Items:

  1. Allaire, F. R. (1977). On reducible configurations for the four colour problem. Winnipeg, Manitoba. Citation info available through ProQuest
  2. Allaire, F., & Swart, E. R. (1978). A systematic approach to the determination of reducible configurations in the four-color conjecture. Journal of Combinatorial Theory, Series B, 25(3), 339–362.  Full-text available online (subscription required) 
  3. Appel, Kenneth, & Haken, W. (1978). The Four-Color Problem. In Mathematics Today Twelve Informal Essays (pp. 153–180). Springer, New York, NY.  Full-text available online (subscription required)
  4. Bigalke, H.-G. (1988). Heinrich Heesch: Kristallgeometrie, Parkettierungen, Vierfarbenforschung. Basel: Birkhauser. Library Catalog Record
  5. Fritsch, R. (1990). Wie wird der Vierfarbensatz bewiesen? Der Mathematische Und Naturwissenschaftliche Unterricht, (43), 80–87. Full-text available online
  6. Gonthier, G. (2005). A computer-checked proof of the four colour theorem.  Full-text available online
  7. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1996). A new proof of the four-colour theorem. Electronic Research Announcements of the American Mathematical Society, 2(1), 17–25. Full-text available online (subscription required) 
  8. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997). Discharging cartwheels.  Full-text available online
  9. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997). Reducibility in the Four-Color Theorem.  Full-text available online 
  10. Steinberger, J. (2010). An unavoidable set of ?-reducible configurations. Transactions of the American Mathematical Society, 362(12), 6633–6661.  Full-text available online (subscription required)
  11. Stromquist, W. R. (1975). Some Aspects of the Four Color Problem. Ann Arbor. Full-text available online
  12. Tymoczko, T. (1979). The Four-Color Problem and Its Philosophical Significance. The Journal of Philosophy, 76(2), 57–83. Full-text available online
  13. Whitney, H., & Tutte, W. T. (1972). Kempe Chains and the Four Colour Problem. In Hassler Whitney Collected Papers (pp. 185–225). Birkhäuser Boston.  Full-text available online (subscription required) 
  14. Wilson, R. (2016). Wolfgang Haken and the four-color problem. Illinois Journal of Mathematics, 60(1), 149–178.  Full-text available online (subscription required)