On Brooks' Theorem for Sparse Graphs-Reference-Cited by-同舟云学术

On Brooks' Theorem for Sparse Graphs

Published:1995-06 Issue:2 Volume:4 Page:97-132
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

Kim Jeong Han

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

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