Tight Bounds on the Clique Chromatic Number

被引：0

作者：

Joret, Gwenael ^{[1
]}

Micek, Piotr ^{[2
]}

Reed, Bruce ^{[3
]}

Smid, Michiel ^{[4
]}

机构：

[1] Univ Libre Bruxelles, Comp Sci Dept, Brussels, Belgium

[2] Jagiellonian Univ, Theoret Comp Sci Dept, Krakow, Poland

[3] McGill Univ, Sch Comp Sci, Montreal, PQ, Canada

[4] Carleton Univ, Sch Comp Sci, Ottawa, ON, Canada

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2021年 / 28卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

GRAPHS;

D O I：

10.37236/9659

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique, which is not an isolated vertex, is monochromatic. We show that every graph of maximum degree Delta has clique chromatic number O (Delta/log Delta). We obtain as a corollary that every n-vertex graph has clique chromatic number O (root n/log n). Both these results are tight.

引用

页数：8

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