Triangle-free graphs with large chromatic number and no induced wheel

被引：1

作者：

Davies, James ^{[1
]}

机构：

[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

来源：

JOURNAL OF GRAPH THEORY | 2023年 / 103卷 / 01期

关键词：

Burling graphs; chromatic number; induced subgraph; wheels; INTERSECTION GRAPHS;

D O I：

10.1002/jgt.22906

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A wheel is a graph consisting of an induced cycle of length at least four and a single additional vertex with at least three neighbours on the cycle. We prove that no Burling graph contains an induced wheel. Burling graphs are triangle-free and have arbitrarily large chromatic number, so this answers a question of Trotignon and disproves a conjecture of Scott and Seymour.

引用

页码：112 / 118

页数：7

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