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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A five-color theorem for graphs on surfaces

Author: Joan P. Hutchinson
Journal: Proc. Amer. Math. Soc. 90 (1984), 497-504
MSC: Primary 05C15; Secondary 05C10
MathSciNet review: 728376
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Abstract: We prove that if a graph embeds on a surface with all edges suitably short, then the vertices of the graph can be five-colored. The motivation is that a graph embedded with short edges is locally a planar graph and hence should not require many more than four colors.

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Additional Information

PII: S 0002-9939(1984)0728376-7
Keywords: Vertex coloring, embedded graph
Article copyright: © Copyright 1984 American Mathematical Society