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On Brooks' Theorem for Sparse Graphs

Published online by Cambridge University Press:  12 September 2008

Jeong Han Kim
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Abstract

Let G be a graph with maximum degree Δ(G). In this paper we prove that if the girth g(G) of G is greater than 4 then its chromatic number, χ(G), satisfies

where o(l) goes to zero as Δ(G) goes to infinity. (Our logarithms are base e.) More generally, we prove the same bound for the list-chromatic (or choice) number:

provided g(G) < 4.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 2 , June 1995 , pp. 97 - 132
Copyright
Copyright © Cambridge University Press 1995

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