Are Four Colors Really Enough?

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


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].


Planar Graph Dual Graph Complete Bipartite Graph Underlying Graph Petersen Graph 
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  1. 1.
    Appel, K. and W. Haken, The solution of the four-color-map problem. Scientific American, 237 (4), 1977, 108–121.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Beineke, L.W. and R.J. Wilson (eds), Selected Topics in Graph Theory 1, 2, Academic Press, London, 1978, 1983.zbMATHGoogle Scholar
  3. 4.
    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.Google Scholar
  4. 3.
    Biggs, N.L., E.K. Lloyd, and R.J. Wilson, Graph Theory1736–1936, Clarendon Press, Oxford, 1986.Google Scholar
  5. 4.
    Clark, J. and D.A. Holton, A First Look at Graph Theory, World Scientific, Singapore, 1996.Google Scholar
  6. 5.
    Isaacs, R., Infinite families of non-trivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly, 82, 1975, 221–239.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 6.
    Fritsch, R. and G. Fritsch, The Four-Color Theorem, translated from the German by J. Peschke, Springer Verlag, New York, 1998.zbMATHCrossRefGoogle Scholar
  8. 7.
    Holton, D.A. and J. Sheehan, The Petersen Graph, Cambridge University Press, Cambridge, 1987.Google Scholar
  9. 8.
    Robertson, N., D.P. Sanders, P.D. Seymour, and R. Thomas, The Four-Color Theorem, J. Comb. Th. (B), 70, 1997, 2-AA. MathSciNetzbMATHCrossRefGoogle Scholar
  10. 9.
    Saaty, T.L. and P.C. Kainen, The Four-Color Problem, McGraw-Hill, New York, 1977.zbMATHGoogle Scholar
  11. 10.
    Wilson, R.J., Introduction to Graph Theory, Third Edition, Longman, Harlow, England, 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

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

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