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.
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页码：2182 / 2187
页数：6
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