An upper bound for the chromatic number of line graphs

被引：13

作者：

King, A. D. ^{[1
]}

Reed, B. A. ^{[1
]}

Vetta, A. ^{[1
]}

机构：

[1] McGill Univ, Sch Comp Sci, Montreal, PQ H3A 2T5, Canada

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2007年 / 28卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1016/j.ejc.2007.04.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was conjectured by Reed [B. Reed, omega, alpha, and chi, Journal of Graph Theory 27 (1998) 177-212] that for any graph G, the graph's chromatic number chi(G) is bounded above by [Delta(G)+1+(omega)(G)/2], where Delta(G) and omega(G) are the rnaximum degree and clique number of G, respectively. In this paper we prove that this hound holds if G is the line graph of a multigraph. The proof yields a polynomial tirne algorithm that takes a line graph G and produces a colouring that achieves our bound. (C) 2007 Published by Elsevier Ltd.

引用

页码：2182 / 2187

页数：6

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