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A 4-chromatic graph with a special plane drawing

Published online by Cambridge University Press:  09 April 2009

Nicholas Wormald
Nicholas Wormald
Affiliation:
Department of Mathematics University of Newcastle Newcastle, N.S.W. 2308, Australia
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Abstract

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A graph is found which is 4-chromatic, has girth 5, and can be obtained by taking a set S of points in the plane and joining two of the points whenever their distance is 1. The points in S are not found explicitly, but their existence is demonstrated by use of a computer.

Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 15, 05 C 10.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 1979

References

Hadwiger, H., Debrunner, H. and Klee, V. (1964), Combinatorial geometry in the plane (Holt, Rinehart & Winston, New York).Google Scholar
Harary, F. (1969), Graph theory (Addison-Wesley, Reading, Mass.).CrossRefGoogle Scholar
Moser, L. and Moser, W. (1961), ‘Solution to problem 10’, Canad. Math. Bull. 4, 187–189.Google Scholar