# Are Four Colors Really Enough?

• Peter Hilton
• Derek Holton
• Jean Pedersen
Part of the Undergraduate Texts in Mathematics book series (UTM)

## 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].

## Keywords

Planar Graph Dual Graph Complete Bipartite Graph Underlying Graph Petersen Graph

## References

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Appel, K. and W. Haken, The solution of the four-color-map problem. Scientific American, 237 (4), 1977, 108–121.
2. 2.
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Fritsch, R. and G. Fritsch, The Four-Color Theorem, translated from the German by J. Peschke, Springer Verlag, New York, 1998.
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Holton, D.A. and J. Sheehan, The Petersen Graph, Cambridge University Press, Cambridge, 1987.Google Scholar
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Robertson, N., D.P. Sanders, P.D. Seymour, and R. Thomas, The Four-Color Theorem, J. Comb. Th. (B), 70, 1997, 2-AA.
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## Authors and Affiliations

• Peter Hilton
• 1
• Derek Holton
• 2
• Jean Pedersen
• 3
1. 1.Mathematical Sciences DepartmentSUNY at BinghamtonBinghamtonUSA
2. 2.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
3. 3.Department of Mathematics and Computer ScienceSanta Clara UniversitySanta ClaraUSA