Abstract
There have been few problems in mathematics over the centuries that have taken the popular imagination as much as the Four Color Problem. Probably the main reason for this is that it is something that can be explained to anybody in only a minute or two. Perhaps the most surprising thing about this problem is that it was invented by a schoolboy and not by a mathematician at all. It’s a very human story — we’ll mention honeymoons, school challenges, and a popular magazine later. We’ll also mention its 124-year history and why some people are still working on it even after it’s been solved. And then there is the famous link between this problem and Lewis Carroll’s poem, “The Hunting of the Snark.” We’ll get to that too. After reading this chapter you might like to look at the overview [1], by Appel and Haken, of their proof of the Four Color Theorem, or, for a more complete treatment, see [6], [7], or [9].
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References
Appel, K. and W. Haken, The solution of the four-color-map problem. Scientific American, 237 (4), 1977, 108–121.
Beineke, L.W. and R.J. Wilson (eds), Selected Topics in Graph Theory 1, 2, Academic Press, London, 1978, 1983.
The figure shows the edges of a regular dodecahedron as viewed up close through one face. This is called the Schlegel diagram of the dodecahedron.
Biggs, N.L., E.K. Lloyd, and R.J. Wilson, Graph Theory1736–1936, Clarendon Press, Oxford, 1986.
Clark, J. and D.A. Holton, A First Look at Graph Theory, World Scientific, Singapore, 1996.
Isaacs, R., Infinite families of non-trivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly, 82, 1975, 221–239.
Fritsch, R. and G. Fritsch, The Four-Color Theorem, translated from the German by J. Peschke, Springer Verlag, New York, 1998.
Holton, D.A. and J. Sheehan, The Petersen Graph, Cambridge University Press, Cambridge, 1987.
Robertson, N., D.P. Sanders, P.D. Seymour, and R. Thomas, The Four-Color Theorem, J. Comb. Th. (B), 70, 1997, 2-AA.
Saaty, T.L. and P.C. Kainen, The Four-Color Problem, McGraw-Hill, New York, 1977.
Wilson, R.J., Introduction to Graph Theory, Third Edition, Longman, Harlow, England, 1983.
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Hilton, P., Holton, D., Pedersen, J. (2002). Are Four Colors Really Enough?. In: Mathematical Vistas. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3681-6_5
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DOI: https://doi.org/10.1007/978-1-4757-3681-6_5
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