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.
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