New upper bounds for the chromatic number of a graph

被引：0

作者：

Stacho, L ^{[1
]}

机构：

[1] Slovak Acad Sci, Inst Math, Dept Informat, Bratislava 84000 4, Slovakia

来源：

JOURNAL OF GRAPH THEORY | 2001年 / 36卷 / 02期

关键词：

simple graph; chromatic number; degree of a vertex;

D O I：

10.1002/1097-0118(200102)36:2<117::AID-JGT6>3.0.CO;2-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for any graph G, the chromatic number chi (G) less than or equal to Delta (2)(G) + 1, where Delta (2)(G) is the largest degree that a vertex nu can have subject to the condition that nu is adjacent to a vertex whose degree is at least as big as its own, Moreover, we show that the upper bound is best possible in the the following sense: If Delta (2)(G) greater than or equal to 3, then to determine whether chi (G) less than or equal to Delta (2)(G) is an NP-complete problem. (C) 2001 John Wiley & Sons, Inc.

引用

页码：117 / 120

页数：4

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