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
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   Math 511.5 AI33G.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=Graphentheorie+eine+Entwicklung+aus+dem+4-Farben+Problem+">zbMATH</a>
2. Aigner, M. (1987). Graph theory: a development from the 4-color problem. Moscow, ID: BCS Associates. Library Catalog Record
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   Math 511.5 AI33G:E.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=Graph+theory+a+development+from+the+4-color+problem">zbMATH</a>
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
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   Math (non-circulating) 519.4 M314P.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=535003">MathSciNet</a>
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).
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   Math (non-circulating) 510.6 AMB2.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-84966228398&origin=resultslist&sort=plf-f&src=s&sid=0685b0fe139a73fc2666aa13952dfd9a&sot=a&sdt=a&sl=41&s=TITLE%28Every+planar+map+is+four+colorable%29&relpos=2&citeCnt=143&searchTerm">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.3690049">Library Catalog Record</a>
5. Appel, K., & Haken, W. (1976). Every planar map is four colorable. Journal of Recreational Mathematics, 9(3), 161. Library Catalog Record
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   Math (non-circulating) 793.7405 JO.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0543797">MathSciNet</a>
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).
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   Math (non-circulating) 510.5 DI.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.523850">Library Catalog Record</a>
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).
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   Math (non-circulating) 510.5 IL.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0392641">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.526688">Library Catalog Record</a>
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).
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   Math (non-circulating) 510.5 IL.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.526688">Library Catalog Record</a>
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).
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   Math (non-circulating) 511.605 JOB.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.557297">Library Catalog Record</a>
10. Appel, K., & Haken, W. (1986). The four color proof suffices. The Mathematical Intelligencer, 8(1), 10–20. 
    Abstract

    Since no one else has communicated any other errors in the published unavoidability proof since 1976 we assume that a misunderstanding of the nature of Schmidt's work was the source of those rumors that seem to have stimulated so much new interest in our work. We would certainly appreciate independent verification of the remaining 60 percent of our unavoidability proof and would be grateful for any information on further bookkeeping (or other) errors whenever such are found.* We have written computer programs preparatory to a thorough com puter verification of all of the material in the microfiche supplements. When this is completed we plan to publish (entirely on paper rather than on microfiche cards) an entire emended version of our original proof including the q-positive bookkeeping. At first thought one might think that we would miss the pleasures of discussing the latest rumors with our colleagues returning from meetings but further consideration leads us to believe that facts have never stopped the propagation of a good rumor and so nothing much will change.
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    Math (non-circulating) 510.5 MAHI.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0004524866&origin=inward&txGid=389fbbe13f8dfaac04dd5a11c198ced5">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.248795">Library Catalog Record</a>
11. Appel, K., & Haken, W. (1989). Every Planar Map is Four Colorable. American Mathematical Society, 98. Full-text available online (subscription required).
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    Math 510.5 CON v.98.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=1025335">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.7270135">Library Catalog Record - E-Resource</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.1592916">Library Catalog Record - Print Copy</a>
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).
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    Math (non-circulating) 510.5 IL.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.526688">Library Catalog Record</a>
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
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    Math 793.74 B21M1987.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=905673">MathSciNet</a>
14. Bar-Natan, D. (1997). Lie algebras and the Four Color Theorem. Combinatorica, 17(1), 43–52. 
    Abstract

    We present a statement about Lie algebras that is equivalent to the Four Color Theorem.
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    Math (non-circulating) 511.605 CO.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0031444041&origin=resultslist&sort=plf-f&src=s&st1=Lie+algebras+and+the+Four+Color+Theorem&st2=&sid=62f09c5d2f2dc8bdce9e509172f26c20&sot=b&sdt=b&sl=54&s=TITLE-ABS-KEY%28Lie+algebras+and+the+Four+Color+Theorem%29&relpos=0&citeCnt=17&searchTerm=">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.520247">Library Catalog Record</a>
15. Bernhart, F. R. (1977). A digest of the four color theorem. Journal of Graph Theory, 1(3), 207-225.
    Abstract

    A major event in 1976 was the announcement that the Four Color Conjecture (4CC) had at long last become the Four Color Theorem (4CT). The proof by W. Haken, K. Appel, and J. Koch is published in the Illinois Journal of Mathematics, and their two‐part article outlines the nature and reliability of the solution. The first section is a readable and informative historical survey. The reminder will appeal chiefly to specialists in graph theory. Although the logic of attack is relatively simple, the need to examine an immense number of individual cases is frustrating. Hopefully this first breakthrough will pave the way for a short elegant proof. For the second section, 1200 hours of computer time was ...
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    Math (non-circulating) 511.505 JO.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-84923857786&origin=resultslist&sort=plf-f&src=s&sid=126b0163027fe2b9936e09e024cb80f1&sot=a&sdt=a&sl=41&s=TITLE%28A+digest+of+the+four+color+theorem%29&relpos=0&citeCnt=3&searchTerm">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.90192">Library Catalog Record</a>
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).
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    Math (non-circulating) 509.05 ARC.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.jstor.org/stable/41133686?seq=1#page_scan_tab_contents">JSTOR - Full text</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-34250146909&origin=inward&txGid=d56aa1813f9fa123544f69cfeac0dd1f">Scopus citation</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0710552">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.18519">Library Catalog Record</a>
17. Biggs, N. L., Lloyd, E. K., & Wilson, R. J. (1976). Graph theory: 1736–1936. Oxford: Clarendon Press. Library Catalog Record
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    Math 511.5 B484G1977.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0444418">MathSciNet</a>
18. Birkhoff, G. D. (1913). The Reducibility of Maps. American Journal of Mathematics, 35(2), 115–128. Full-text available online (subscription required).
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    Math (non-circulating) 510.5 AJ.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.538094">Library Catalog Record</a>
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).
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    Math (non-circulating) 510.5 AM.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.3560288">Library Catalog Record</a>
20. Chartrand, G., & Lesniak, L. (2005). Graphs & digraphs (4th ed.). Boca Raton: Chapman & Hall/CRC. Library Catalog Record
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    Math 511.5 C385G2005.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR2107429">MathSciNet</a>
21. Dailey, D. P. (1980). Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete. Discrete Mathematics, 30(3), 289–293. 
    Abstract

    It is shown that two sorts of problems belong to the NP-complete class. First, it is proven that for a given κ-colorable graph and a given κ-coloring of that graph, determining whether the graph is or is not uniquely κ-colorable is NP-complete. Second, a result by Garey, Johnson, and Stockmeyer is extended with a proof that the coloring of four-regular planar graphs is NP-complete.
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    Math (non-circulating) 510.5 DI.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0344351687&origin=inward&txGid=60ce5f367f1332ba6c34be2a184b0e4e">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.523850">Library Catalog Record</a>
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
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    Math 511.6 D62P.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0120649">MathSciNet</a>
23. Dowek, G., Guillot, P., & Roman, M. (2015). Computation, proof, machine: Mathematics enters a new age (1st ed.). New York, NY: Cambridge University Press.
    Abstract

    Computation is revolutionizing our world, even the inner world of the “pure” mathematician. Mathematical methods – especially the notion of proof–that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms – all have played an important role in mathematical progress from the beginning – but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation ...
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    Math 510.9 D753c.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-84953232404&origin=resultslist&sort=plf-f&src=s&st1=Computation%2c+proof%2c+machine%3a+mathematics+enters+a+new+age+&st2=&sid=ce8e2633ced4c665eaaf53a0a2756c2c&sot=b&sdt=b&sl=73&s=TITLE-ABS-KEY%28Computation%2c+proof%2c+machine%3a+mathematics+enters+a+new+age+%29&relpos=0&citeCnt=1&searchTerm">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.8039731">Library Catalog Record - E-Resource</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.7791021">Library Catalog Record - Print Copy</a>
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
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    Math 511.6 D993M:G.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0576573">MathSciNet</a>
25. Errera, A. (1927). Exposé historique du problème des quatre couleurs. Periodico di Matematiche. IV. Serie, 7, 20–41. Library Catalog Record
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    Math 514 ER7E.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=Expose%CC%81+historique+du+proble%CC%80me+des+quatre+couleurs">zbMATH</a>
26. Fritsch, R. (1994). Der Vierfarbensatz: Geschichte, topologische Grundlagen, und Beweisidee. Mannheim: B.I.-Wissenschaftsverlag. Library Catalog Record
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    Math 514 F918V.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR1270673">MathSciNet</a>
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).
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    Math 514 F918v:E.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.7841187">Library Catalog Record - E-Resource</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.4100061">Library Catalog Record - Print Copy</a>
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).
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    Math (non-circulating) 510.6 AMN.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=2463991">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.137577">Library Catalog Record</a>
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).
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    Math (non-circulating) 506 REP.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.2569496">Library Catalog Record</a>
30. Hadwiger, H. (1943). Über eine Klassifickation der Strekenkomplexe. In Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich (Vol. 88). Zürich: Fäsi & Beer. Library Catalog Record
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    Oak Street Library 506 ZU.
31. Haken, W. (1977). An attempt to understand the four color problem. Journal of Graph Theory, 1(3), 193-206.
    Abstract

    Is the recently obtained, computer‐aided proof of the Four Color Theorem an isolated phenomenon or is its combinatorial complexity typical for a significantly large class of mathematical problems? While it is too early to give a definite answer to this question, an informal discussion is undertaken in this article.
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    Math (non-circulating) 511.505 JO.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-84926406020&origin=inward&txGid=503af0e0c2c5756ac04d41bd0b960929">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.90192">Library Catalog Record</a>
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
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    Math (non-circulating) 510.6 INT.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR562712">MathSciNet</a>
33. Heawood, P. J. (1890). Map-colour theorem. The Quarterly Journal of Pure and Applied Mathematics, 24, 332–338. Library Catalog Record
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    Math (non-circulating) 510.5 QU.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=an%3A22.0562.02">zbMATH</a>
34. Heawood, P. J. (1949). Map-colour theorem. Proceedings of the London Mathematical Society, 2(51), 161-175. Full-text available online (subscription required).
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    Math (non-circulating) 510.6 LMSER.2.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-84963089152&origin=resultslist&sort=plf-f&src=s&sid=1591e4a7e25802ee6667a38607d76ac6&sot=a&sdt=a&sl=51&s=AUTHLASTNAME%28Heawood%29+AND+TITLE%28Map-colour+theorem%29&relpos=0&citeCnt=5&searchTerm">Scopus citation</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=0030735">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.117831">Library Catalog Record</a>
35. Heesch, H. (1969). Untersuchungen zum Vierfarbenproblem (Vol. 810). Mannheim: Bibliographisches Institut. Library Catalog Record
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    Math 511.64 H36U.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0248048">MathSciNet</a>
36. Hitotsumatsu, S. (1978). Shishiki mondai: sono tanjō kara kaiketsu made. Tōkyō: Kōdansha, cShōwa 53. Library Catalog Record
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    Oak Street Library (request online) QA612.19 .H57X.
37. Hudson, H. (2003). Four Colors Do Not Suffice. The American Mathematical Monthly, 110(5), 417–423. Full-text available online (subscription required).
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    Oak Street BTAA Shared Print Repository (non-circulating) 510.5 AM.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0037648651&origin=resultslist&sort=plf-f&src=s&sid=b2ef7990f48a2e47fa9c0f3a63a07742&sot=a&sdt=a&sl=33&s=TITLE%28Four+colors+do+not+suffice%29&relpos=0&citeCnt=4&searchTerm">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.3560288">Library Catalog Record</a>
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. 
    Abstract

    This paper discusses combinatorial recoupling theory and generalisations of spin recoupling theory, first in relation to the vector cross product algebra and a reformulation of the Four Color Theorem, and secondly in relation to the Temperley Lieb algebra, Spin Networks, the Jones polynomial and the SU(2) 3-Manifold invariants of Witten, Reshetikhin and Turaev. We emphasize the roots of these ideas in the Penrose theory of spin networks.
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    Math 514.224 B7311994.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://doi.org/10.1142/9789812798275_0009">World Scientific</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=1338596">MathSciNet</a>
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).
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    Oak Street Library (request online) 511.6 K81C.<br /> See also:<br /> <a href="https://hdl.handle.net/2027/uiuo.ark:/13960/t4mk7tw12">HathiTrust Digital Library</a><br /> <a href="https://archive.org/details/computationoffou802koch">Internet Archive</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.555136">Library Catalog Record</a>
40. May, K. O. (1965). The Origin of the Four-Color Conjecture. Isis, 56(3), 346–348. Full-text available online (subscription required).
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    Oak Street Library 505 ISI.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=http://www.jstor.org/stable/228109">JSTOR - Full-text</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.3692072">Library Catalog Record</a>
41. Mayer, J. (1974). Nouvelles réduction dans le problème des quatre couleurs. Montpellier: Université des sciences et techniques du Languedoc, U. E. R. de mathématiques. Library Catalog Record
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    MathQ. 511.6 M452N .<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0382055">MathSciNet</a>
42. Nash-Williams, C. S. J. A. (1967). Infinite graphs – A survey. Journal of Combinatorial Theory, 3(3), 286–301. 
    Abstract

    This expository article describes work which has been done on various problems involving infinite graphs, mentioning also a few unsolved problems or suggestions for future investigation.
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    Math (non-circulating) 511.605 JO.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-8844276124&origin=resultslist&sort=plf-f&src=s&st1=Infinite+graphs-A+survey&st2=&sid=b7594660e16c30cdf609f69608cac5c5&sot=b&sdt=b&sl=39&s=TITLE-ABS-KEY%28Infinite+graphs-A+survey%29&relpos=4&citeCnt=38&searchTerm=">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.557462">Library Catalog Record</a>
43. Nelson, R., & Wilson, R. (1990). Graph colourings. Essex, England: Longman. Library Catalog Record
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    Math 512.55 G767.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://doi.org/10.1017/S0025557200147990">Cambridge Core</a>
44. Ore, Ø. (1967). The four-color problem. New York-London: Academic Press. Full-text available online (subscription required). 
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    Math 514 OR3F.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=an%3A0149.21101">zbMATH</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.719527">Library Catalog Record</a>
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).
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    Math 511.5 OS2E.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.559180">Library Catalog Record</a>
46. Robertson, N., Sanders, D., Seymour, P., & Thomas, R. (1997). The Four-Colour Theorem. Journal of Combinatorial Theory, Series B, 70(1), 2–44. 
    Abstract

    The four-colour theorem, that every loopless planar graph admits a vertex-colouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we give another proof, still using a computer, but simpler than Appel and Haken's in several respects.
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    Math (non-circulating) 511.605 JOB.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0031146074&origin=resultslist&sort=plf-f&src=s&sid=1af679ad5b526f44740c29775e368213&sot=a&sdt=a&sl=58&s=AUTHLASTNAME%28Robertson%29+AND+TITLE%28The+four-colour+theorem%29&relpos=0&citeCnt=278&searchTerm">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.557297">Library Catalog Record</a>
47. Saaty, T. L., & Kainen, P. C. (1986). The four-color problem: assaults and conquest. New York : Dover Publications. Library Catalog Record
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    Math 511.5 SA12F1986.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0863420">MathSciNet</a>
48. Stewart, I. (2013). Visions of Infinity: The Great Mathematical Problems. New York, NY: Basic Books. Library Catalog Record
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    Math 510 St494v
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).
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    Math (non-circulating) 510.5 AM.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.3560288">Library Catalog Record</a>
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).
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    Math (non-circulating) 506 REP.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.2569496">Library Catalog Record</a>
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).
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    Math (non-circulating) 506 REP.<br /> See also:<br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.2569496">Library Catalog Record</a>
52. Thomas, J. M. (1971). The four color theorem (Rev. ed.). Philadelphia. Library Catalog Record
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    Main Stacks 511.6 T364F1971.
53. Thomas, J. M. (1977). The four color theorem (Final ed.). Durham, N.C. Library Catalog Record
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    Math 511.6 T364F.
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).
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    Math (non-circulating) 510.6 AMN.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=1633714">MathSciNet</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.137577">Library Catalog Record</a>
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
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    Math 511.6 B777s1999.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR1724997">MathSciNet</a>
56. Wernicke, P. (1904). Über den kartographischen Vierfarbensatz. Mathematische Annalen, 58(3), 413–426. Full-text available online (subscription required).
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    Math (non-circulating) 510.5 MH.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0040889316&origin=resultslist&sort=plf-f&src=s&sid=b42c419c992f9eaa5e5401f56db748b1&sot=a&sdt=a&sl=42&s=AUTHLASTNAME%28Wernicke%29+AND+TITLE%28Uber+den%29&relpos=0&citeCnt=76&searchTerm=">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.535077">Library Catalog Record</a>
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).
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    Math (non-circulating) 510.905 HI.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-27744556343&origin=inward&txGid=bc14271ac4c3729bcc99111dc7f836fe">Scopus citation</a><br /> <a href="https://i-share.carli.illinois.edu/vf-uiu/Record/UIUdb.18553">Library Catalog Record</a>
58. Wilson, R. A. (2002). Graphs, colourings and the four-colour theorem. Oxford: Oxford University Press. Library Catalog Record
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    Math W691g.<br /> See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://doi.org/10.1017/S0025557200172572">Cambridge Core</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR1888337">MathSciNet</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=Graphs%2C+colourings+and+the+four-colour+theorem">zbMATH</a>
59. Wilson, R. J. (2002). Four colours suffice: how the map problem was solved. Princeton, NJ: Princeton University Press. Library Catalog Record
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    Main Stacks 793.74 W691f.
60. Wilson, R. J. (2014). Four colours suffice: how the map problem was solved. Princeton, NJ: Princeton University Press. Library Catalog Record
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    Math 793.74 W691f2014.

Additional Items:

67. Allaire, F. R. (1977). On reducible configurations for the four colour problem. Winnipeg, Manitoba. Citation info available through ProQuest
68. 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.
    Abstract

    Reducibility of configurations is determined by an algorithm programmed on a computer. The effectiveness of the program is improved after implementing results obtained by investigating the algebraic structure of the problem. A comprehensive list of reducible configurations up to the 10-ring level is tabled.
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    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-0010998868&origin=inward&txGid=f6b3c5029677300130eb1c699cd44f77">Scopus citation</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0516267">MathSciNet</a>
69. Appel, Kenneth, & Haken, W. (1978). The Four-Color Problem. In Mathematics Today Twelve Informal Essays (pp. 153–180). Springer, New York, NY. 
    Abstract

    In 1976, the Four-Color Problem was solved: every map drawn on a sheet of paper can be colored with only four colors in such a way that countries sharing a common border receive different colors. This result was of interest to the mathematical community since many mathematicians had tried in vain for over a hundred years to prove this simple-sounding statement. Yet among mathematicians who were not aware of the developments leading to the proof, the outcome had rather dismaying aspects, for the proof made unprecedented use of computer computation; the correctness of the proof cannot be checked without the aid of a computer. Moreover, adding to the strangeness of the proof, some of the crucial ideas were perfected by ...
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    See also:<br /> <a href="https://i-share-uiu.primo.exlibrisgroup.com/permalink/01CARLI_UIU/gpjosq/alma994145612205899">Library Catalog Record</a>
70. Bigalke, H.-G. (1988). Heinrich Heesch: Kristallgeometrie, Parkettierungen, Vierfarbenforschung. Basel: Birkhauser. Library Catalog Record
71. Fritsch, R. (1990). Wie wird der Vierfarbensatz bewiesen? Der Mathematische Und Naturwissenschaftliche Unterricht, (43), 80–87. Full-text available online
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    See also:<br /> <a href="https://zbmath.org/?q=Wie+wird+der+Vierfarbensatz+bewiesen+Der+Mathematische+Und+Naturwissenschaftliche+Unterricht">zbMATH</a>
72. Gonthier, G. (2005). A computer-checked proof of the four colour theorem. 
    Abstract

    This report gives an account of a successful formalization of the proof of the Four Colour Theorem, which was fully checked by the Coq v7.3.1 proof assistant (13). This proof is largely based on the mixed mathematics/computer proof (26) of Robertson et al, but contains original contributions as well. This document is organized as follows: section 1 gives a historical introduction to the problem and positions our work in this setting; section 2 defines more precisely what was proved; section 3 explains the broad outline of the proof; section 4 explains how we exploited the features of the Coq assistant to conduct the proof, and gives a brief description of ...
     Full-text available online
73. 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.
    Abstract

    The four-colour theorem, that every loopless planar graph admits a vertex-colouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we announce another proof, still using a computer, but simpler than Appel and Haken's in several respects.
    Full-text available online (subscription required) 
    More Info

    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR1405965">MathSciNet</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://zbmath.org/?q=an%3A0865.05039">zbMATH</a>
74. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997). Discharging cartwheels.
    Abstract

    In (J. Combin. Theory Ser. B 70 (1997), 2-44) we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have verified those statements using a computer. Here we give additional details for one of those lemmas, and we include the original computer programs and data as "ancillary files" accompanying this submission.
     Full-text available online
75. Robertson, N., Sanders, D. P., Seymour, P., & Thomas, R. (1997). Reducibility in the Four-Color Theorem.
    Abstract

    In (J. Combin. Theory Ser. B 70 (1997), 2-44) we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have verified those statements using a computer. Here we give additional details for one of those lemmas, and we include the original computer programs and data as "ancillary files" accompanying this submission.
     Full-text available online 
    More Info

    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR2626882">MathSciNet</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://search.proquest.com/docview/302854767?accountid=14553">ProQuest
76. Steinberger, J. (2010). An unavoidable set of ?-reducible configurations. Transactions of the American Mathematical Society, 362(12), 6633–6661.
    Abstract

    We give a new proof of the four-color theorem by exhibiting an unavoidable set of 2822 ?-reducible configurations. The existence of such a set had been conjectured by several researchers including Stromquist (1975), Appel and Haken (1977), and Robertson, Sanders, Seymour and Thomas (1997).
     Full-text available online (subscription required)
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    See also:<br /> <a href="https://www.library.illinois.edu/proxy/go.php?url=https://www.jstor.org/stable/40997219?seq=1#page_scan_tab_contents">JSTOR - Full text</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-78650292585&origin=inward&txGid=29a62d3ec95cb4d2a666adfd1800afc9">Scopus ciation</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR2678989">MathSciNet</a><br /> <a href="https://zbmath.org/?q=An+unavoidable+set+of+D-reducible+configurations">zbMATH</a><br /> <a href="https://arxiv.org/abs/0905.0043">arXiv.org</a>
77. Stromquist, W. R. (1975). Some Aspects of the Four Color Problem. Ann Arbor. Full-text available online
    More Info

    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR2940609">MathSciNet</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://search.proquest.com/docview/302781374">ProQuest
78. Tymoczko, T. (1979). The Four-Color Problem and Its Philosophical Significance. The Journal of Philosophy, 76(2), 57–83. Full-text available online
    More Info

    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.jstor.org/stable/2025976?&seq=1#page_scan_tab_contents">JSTOR - Full text</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR900161">MathSciNet</a>
79. Whitney, H., & Tutte, W. T. (1972). Kempe Chains and the Four Colour Problem. In Hassler Whitney Collected Papers (pp. 185–225). Birkhäuser Boston. 
    Abstract

    In October 1971 the combinatorial world was swept by the rumour that the notorious Four Colour Problem had at last been solved, - that with the help of a computer it had been demonstrated that any map in the plane can be coloured with at most four - colours so that no two countries with a common boundary line are given the same colour.
    Full-text available online (subscription required) 
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    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR0309782">MathSciNet</a><br /> <a href="https://zbmath.org/?q=an%3A0253.05120">zbMATH</a>
80. Wilson, R. (2016). Wolfgang Haken and the four-color problem. Illinois Journal of Mathematics, 60(1), 149–178. 
    Abstract

    In 1852, Augustus De Morgan, Professor of Mathematics at University College, London, was asked: Can every map be colored with just four colors in such a way that neighboring countries are colored differently? Over a century later, in a controversial proof that made substantial use of a computer, Wolfgang Haken and Kenneth Appel of the University of Illinois answered the question in the affirmative. But how did Haken come to be involved with the problem, and what was his role in its solution?
     Full-text available online (subscription required) 
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    See also:<br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://www.scopus.com/record/display.uri?eid=2-s2.0-85021210437&origin=resultslist&sort=plf-f&src=s&st1=Wolfgang+Haken+and+the+four-color+problem&st2=&sid=1a7b3fe8b897bd80b65b85e6e7a69b1f&sot=b&sdt=b&sl=56&s=TITLE-ABS-KEY%28Wolfgang+Haken+and+the+four-color+problem%29&relpos=1&citeCnt=0&searchTerm=">Scopus citation</a><br /> <a href="http://www.library.illinois.edu/proxy/go.php?url=https://mathscinet.ams.org/mathscinet-getitem?mr=MR3665176">MathSciNet</a>