{"id":1713,"date":"2018-08-04T14:03:00","date_gmt":"2018-08-04T14:03:00","guid":{"rendered":"http:\/\/wordpress.library.illinois.edu\/mtx\/?page_id=1713"},"modified":"2025-11-12T19:35:33","modified_gmt":"2025-11-12T19:35:33","slug":"four-color-theorem-resources","status":"publish","type":"page","link":"https:\/\/wordpress.library.illinois.edu\/mtx\/four-color-theorem-resources\/","title":{"rendered":"Four Color Theorem (4CT) – Resources"},"content":{"rendered":"

Print and online copies<\/span><\/h2>\n

Items on Display:<\/strong><\/h3>\n
    \n
  1. Aigner, M. (1984).\u00a0Graphentheorie: eine Entwicklung aus dem 4-Farben Problem<\/i>.\u00a0Stuttgart:\u00a0B.G. Teubner.<\/a>\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  2. Aigner, M. (1987).\u00a0Graph theory: a development from the 4-color problem.\u00a0<\/i>Moscow, ID: BCS Associates.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  3. Allaire, F. (1978). Another proof of the four colour theorem. I. In Proceedings of the Seventh Manitoba Conference on Numerical Mathematics and Computing <\/em>(pp. 3\u201372).<\/em>Winnipeg:\u00a0Utilitas Mathematica Publishing. Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  4. Appel, K., & Haken, W. (1976). Every planar map is four colorable.\u00a0Bulletin of the American Mathematical Society<\/i>,\u00a082<\/i>(5), 711\u2013712.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  5. Appel, K., & Haken, W. (1976). Every planar map is four colorable.\u00a0Journal of Recreational Mathematics<\/i>,\u00a09<\/i>(3), 161.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  6. Appel, K., & Haken, W. (1976). Special announcement: A proof of the four color theorem.\u00a0Discrete Mathematics<\/i>,\u00a016<\/i>(2), 179\u2013180.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  7. Appel, K., & Haken, W. (1976). The existence of unavoidable sets of geographically good configurations.\u00a0Illinois Journal of Mathematics<\/i>,\u00a020<\/i>(2), 218\u2013297.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  8. Appel, K., & Haken, W. (1977). Every planar map is four colorable. Part I: Discharging.\u00a0Illinois Journal of Mathematics<\/i>,\u00a021<\/i>(3), 429\u2013490.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  9. Appel, K, & Haken, W. (1979). An unavoidable set of configurations in planar triangulations.\u00a0Journal of Combinatorial Theory, Series B<\/i>,\u00a026<\/i>(1), 1\u201321.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  10. Appel, K., & Haken, W. (1986). The four color proof suffices.\u00a0The Mathematical Intelligencer<\/i>,\u00a08<\/i>(1), 10\u201320.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  11. Appel, K., & Haken, W. (1989). Every Planar Map is Four Colorable. American Mathematical Society, 98<\/em>. Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  12. Appel, K., Haken, W., & Koch, J. (1977). Every planar map is four colorable. Part II: Reducibility.\u00a0Illinois Journal of Mathematics<\/i>,\u00a021<\/i>(3), 491\u2013567.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  13. Ball, W. W. R., & Coxeter, H. S. M. (1987).\u00a0Map-colouring problems. In\u00a0W. W. R. Ball & H. S. M. Coxeter,\u00a0Mathematical recreations and essays\u00a0<\/i>(13th ed., p. 222). New York:\u00a0Dover Publications.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  14. Bar-Natan, D. (1997). Lie algebras and the Four Color Theorem.\u00a0Combinatorica<\/i>,\u00a017<\/i>(1), 43\u201352.\u00a0<\/span><\/a> Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  15. Bernhart, F. R. (1977). A digest of the four color theorem. Journal of Graph Theory, 1<\/em>(3), 207-225. <\/span><\/a> Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  16. Biggs, N. L. (1983). De morgan on map colouring and the separation axiom. Archive for History of Exact Sciences, 28<\/em>(2), 165\u2013170. Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  17. Biggs, N. L., Lloyd, E. K., & Wilson, R. J. (1976).\u00a0Graph theory: 1736\u20131936<\/i>. Oxford: Clarendon Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  18. Birkhoff, G. D. (1913). The Reducibility of Maps.\u00a0American Journal of Mathematics<\/i>,\u00a035<\/i>(2), 115\u2013128.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  19. Burger, E. B., & Morgan, F. (1997). Fermat\u2019s Last Theorem, the Four Color Conjecture, and Bill Clinton for April Fools\u2019 Day.\u00a0The American Mathematical Monthly<\/i>,\u00a0104<\/i>(3), 246\u2013255.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  20. Chartrand, G., & Lesniak, L. (2005).\u00a0Graphs & digraphs<\/i>\u00a0(4th ed.). Boca Raton:\u00a0Chapman & Hall\/CRC.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  21. Dailey, D. P. (1980). Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete.\u00a0Discrete Mathematics<\/i>,\u00a030<\/i>(3), 289\u2013293.\u00a0<\/span><\/a> Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  22. Dirac, G. A., & Stojakovi\u0107, M. D. (1960).\u00a0Problem \u010detiri boje\u00a0<\/i>(Vol. 16). Beograd: Katedra za matematiku Elektrotehnic\u030ckog fakulteta univerziteta u Beogradu.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  23. Dowek, G., Guillot, P., & Roman, M. (2015). Computation, proof, machine: Mathematics enters a new age<\/em> (1st ed.). New York, NY: Cambridge University Press. Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  24. Dynkin, E. B., & Uspenski, W. A. (1979). Mathematische Unterhaltungen: Aufgaben u\u0308ber das Mehrfarbenproblem, aus der Zahlentheorie und der Wahrscheinlichkeitsrechnung.\u00a0Ko\u0308ln:\u00a0Aulis Verlag Deubner.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  25. Errera, A. (1927). Expos\u00e9 historique du probl\u00e8me des quatre couleurs.\u00a0Periodico di Matematiche. IV. Serie<\/i>,\u00a07<\/i>, 20\u201341.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  26. Fritsch, R. (1994). Der Vierfarbensatz: Geschichte, topologische Grundlagen, und Beweisidee. <\/em>Mannheim:\u00a0B.I.-Wissenschaftsverlag.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  27. Fritsch, R., & Fritsch, G. (1998).\u00a0The Four-Color Theorem:\u00a0History, Topological Foundations, and Idea of Proof<\/i>. New York, NY: Springer New York.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  28. Gonthier, G. (2008). Formal Proof \u2013 The Four-Color Theorem. Notices of the American Mathematical Society,\u00a055<\/em>(11), 1382\u20131393.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  29. Guthrie, F. (1880). 9. Note on the Colouring of Maps. In\u00a0Proceedings of the Royal Society of Edinburgh<\/i>,\u00a010<\/i>, 727\u2013728.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  30. Hadwiger, H. (1943). \u00dcber eine Klassifickation der Strekenkomplexe. In Vierteljahrsschrift der Naturforschenden Gesellschaft in Z\u00fcrich<\/em> (Vol. 88).\u00a0Zu\u0308rich:\u00a0Fa\u0308si & Beer.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  31. Haken, W. (1977). An attempt to understand the four color problem. Journal of Graph Theory, 1<\/em>(3), 193-206. <\/span><\/a> Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  32. Haken, W. (1980). Combinatorial aspects of some mathematical problems. In Proceedings of the International Congress of Mathematicians <\/em>(pp. 953\u2013961). Toronto:\u00a0University of Toronto Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  33. Heawood, P. J. (1890). Map-colour theorem.\u00a0The Quarterly Journal of Pure and Applied Mathematics<\/i>,\u00a024<\/i>, 332\u2013338.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  34. Heawood, P. J. (1949). Map-colour theorem.\u00a0Proceedings of the London Mathematical Society,\u00a0<\/i>2<\/i>(51), 161-175.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  35. Heesch, H. (1969).\u00a0Untersuchungen zum Vierfarbenproblem<\/i>\u00a0(Vol. 810). Mannheim:\u00a0Bibliographisches Institut.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  36. Hitotsumatsu, S. (1978).\u00a0Shishiki mondai: sono tanj\u014d kara kaiketsu made.\u00a0<\/i>To\u0304kyo\u0304:\u00a0Ko\u0304dansha, cSho\u0304wa 53.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  37. Hudson, H. (2003). Four Colors Do Not Suffice.\u00a0The American Mathematical Monthly<\/i>,\u00a0110<\/i>(5), 417\u2013423.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  38. Kauffman, L. H. (1994).\u00a0Spin networks, topology and discrete physics. In Yang, C. N., & Ge, M. L. (Eds.),\u00a0Braid group, knot theory and statistical mechanics. II<\/i>\u00a0(Vol. 17, pp. 234\u2013274<\/span>). River Edge, NJ: World Scientific Publishing Co., Inc.\u00a0<\/span><\/a>\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  39. Koch, J. A. (1976). Computation of four color irreducibility<\/em>. Urbana: Department of Computer Science, University of Illinois at Urbana-Champaign. Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  40. May, K. O. (1965). The Origin of the Four-Color Conjecture.\u00a0Isis<\/i>,\u00a056<\/i>(3), 346\u2013348.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  41. Mayer, J. (1974).\u00a0Nouvelles r\u00e9duction dans le probl\u00e8me des quatre couleurs<\/i>. Montpellier:\u00a0Universite\u0301 des sciences et techniques du Languedoc, U. E. R. de mathe\u0301matiques.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  42. Nash-Williams, C. S. J. A. (1967). Infinite graphs \u2013 A survey.\u00a0Journal of Combinatorial Theory<\/i>,\u00a03<\/i>(3), 286\u2013301.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  43. Nelson, R., & Wilson, R. (1990).\u00a0Graph colourings<\/i>. Essex, England:\u00a0Longman.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  44. Ore, \u00d8. (1967).\u00a0The four-color problem<\/i>.\u00a0New York-London: Academic Press. Full-text available online<\/a> (subscription required).\u00a0<\/span><\/a><\/li>\n
  45. Osgood, T. W. (1973).\u00a0An Existence Theorem for Planar Triangulations With Vertices of Degree Five, Six, and Eight<\/i>. University of Illinois at Urbana-Champaign.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  46. Robertson, N., Sanders, D., Seymour, P., & Thomas, R. (1997). The Four-Colour Theorem.\u00a0Journal of Combinatorial Theory, Series B<\/i>,\u00a070<\/i>(1), 2\u201344.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  47. Saaty, T. L., & Kainen, P. C. (1986).\u00a0The four-color problem:\u00a0assaults and conquest.\u00a0<\/i>New York :\u00a0Dover Publications.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  48. Stewart, I. (2013). Visions of Infinity: The Great Mathematical Problems<\/em>. New York, NY:\u00a0Basic Books.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  49. Swart, E. R. (1980). The Philosophical Implications of the Four-Color Problem.\u00a0The American Mathematical Monthly<\/i>,\u00a087<\/i>(9), 697\u2013707.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  50. Tait. (1880). 4. On the Colouring of Maps. In\u00a0Proceedings of the Royal Society of Edinburgh<\/i>,\u00a010<\/i>, 501\u2013503.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  51. Tait. (1880). 10. Remarks on the previous Communication. In\u00a0Proceedings of the Royal Society of Edinburgh<\/i>,\u00a010<\/i>, 729\u2013729.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  52. Thomas, J. M. (1971).\u00a0The four color theorem<\/i>\u00a0(Rev. ed.).\u00a0Philadelphia.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  53. Thomas, J. M. (1977).\u00a0The four color theorem<\/i>\u00a0(Final ed.).\u00a0Durham, N.C. Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  54. Thomas, R. (1998). An Update on the Four-Color Theorem.\u00a0Notices of the American Mathematical Society, 45<\/em>(7), 848-859.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  55. Thomas, R. (1999). Recent excluded minor theorems for graphs. In\u00a0J. D. Lamb, & D. A. Preece (Eds.),\u00a0Surveys in combinatorics, 1999 <\/i>(Vol. 267, pp.\u00a0201\u2013222<\/span>). New York:\u00a0Cambridge University Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  56. Wernicke, P. (1904). \u00dcber den kartographischen Vierfarbensatz.\u00a0Mathematische Annalen<\/i>,\u00a058<\/i>(3), 413\u2013426.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  57. Wilson, J. (1976). New light on the origin of the four-color conjecture.\u00a0Historia Mathematica<\/i>,\u00a03<\/i>(3), 329\u2013330.\u00a0Full-text available online<\/a> (subscription required). <\/span><\/a><\/li>\n
  58. Wilson, R. A. (2002).\u00a0Graphs, colourings and the four-colour theorem<\/i>. Oxford: Oxford University Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  59. Wilson, R. J. (2002).\u00a0Four colours suffice: how the map problem was solved.<\/i> Princeton, NJ: Princeton University Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n
  60. Wilson, R. J. (2014).\u00a0Four colours suffice: how the map problem was solved.<\/i> Princeton, NJ: Princeton University Press.\u00a0Library Catalog Record<\/a> <\/span><\/a><\/li>\n<\/ol>\n

    Additional Items:<\/strong><\/h3>\n
      \n
    1. Allaire, F. R. (1977).\u00a0On reducible configurations for the four colour problem<\/i>. Winnipeg, Manitoba.\u00a0Citation info available through\u00a0ProQuest<\/a><\/li>\n
    2. Allaire, F., & Swart, E. R. (1978). A systematic approach to the determination of reducible configurations in the four-color conjecture.\u00a0Journal of Combinatorial Theory, Series B<\/i>,\u00a025<\/i>(3), 339\u2013362. <\/span><\/a>\u00a0Full-text available online<\/a> (subscription required)\u00a0<\/span><\/a><\/li>\n
    3. Appel, Kenneth, & Haken, W. (1978). The Four-Color Problem. In\u00a0Mathematics Today Twelve Informal Essays<\/i>\u00a0(pp. 153\u2013180). Springer, New York, NY.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a>\u00a0(subscription required) <\/span><\/a><\/li>\n
    4. Bigalke, H.-G. (1988).\u00a0Heinrich Heesch: Kristallgeometrie, Parkettierungen, Vierfarbenforschung<\/i>. Basel: Birkhauser.\u00a0Library Catalog Record<\/a><\/li>\n
    5. Fritsch, R. (1990). Wie wird der Vierfarbensatz bewiesen?\u00a0Der Mathematische Und Naturwissenschaftliche Unterricht<\/i>, (43), 80\u201387. Full-text available online<\/a> <\/span><\/a><\/li>\n
    6. Gonthier, G. (2005).\u00a0A computer-checked proof of the four colour theorem<\/i>.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a><\/li>\n
    7. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1996). A new proof of the four-colour theorem.\u00a0Electronic Research Announcements of the American Mathematical Society<\/i>,\u00a02<\/i>(1), 17\u201325. <\/span><\/a> Full-text available online<\/a> (subscription required)\u00a0<\/span><\/a><\/li>\n
    8. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997).\u00a0Discharging cartwheels<\/i>. <\/span><\/a>\u00a0Full-text available online<\/a><\/li>\n
    9. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997).\u00a0Reducibility in the Four-Color Theorem<\/i>. <\/span><\/a>\u00a0Full-text available online<\/a>\u00a0<\/span><\/a><\/a><\/li>\n
    10. Steinberger, J. (2010). An unavoidable set of ?-reducible configurations.\u00a0Transactions of the American Mathematical Society<\/i>,\u00a0362<\/i>(12), 6633\u20136661. <\/span><\/a>\u00a0Full-text available online<\/a>\u00a0(subscription required) <\/span><\/a><\/li>\n
    11. Stromquist, W. R. (1975).\u00a0Some Aspects of the Four Color Problem<\/i>. Ann Arbor. Full-text available online<\/a> <\/span><\/a><\/a><\/li>\n
    12. Tymoczko, T. (1979). The Four-Color Problem and Its Philosophical Significance.\u00a0The Journal of Philosophy<\/i>,\u00a076<\/i>(2), 57\u201383.\u00a0Full-text available online<\/a> <\/span><\/a><\/li>\n
    13. Whitney, H., & Tutte, W. T. (1972). Kempe Chains and the Four Colour Problem. In\u00a0Hassler Whitney Collected Papers<\/i>\u00a0(pp. 185\u2013225). Birkh\u00e4user Boston.\u00a0<\/span><\/a> Full-text available online<\/a> (subscription required)\u00a0<\/span><\/a><\/li>\n
    14. Wilson, R. (2016). Wolfgang Haken and the four-color problem.\u00a0Illinois Journal of Mathematics<\/i>,\u00a060<\/i>(1), 149\u2013178.\u00a0<\/span><\/a>\u00a0Full-text available online<\/a>\u00a0(subscription required)\u00a0<\/span><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      Print and online copies Items on Display: Aigner, M. (1984).\u00a0Graphentheorie: eine Entwicklung aus dem 4-Farben Problem.\u00a0Stuttgart:\u00a0B.G. Teubner.\u00a0Library Catalog Record Aigner, M. (1987).\u00a0Graph theory: a development from the 4-color problem.\u00a0Moscow, ID: BCS Associates.\u00a0Library Catalog Record Allaire, F. (1978). Another proof of the four colour theorem. I. In Proceedings of the Seventh Manitoba Conference on Numerical Mathematics […]<\/p>\n","protected":false},"author":296,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1713","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/1713","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/users\/296"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/comments?post=1713"}],"version-history":[{"count":24,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/1713\/revisions"}],"predecessor-version":[{"id":4001,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/1713\/revisions\/4001"}],"wp:attachment":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/media?parent=1713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}