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
收藏
页码：112 / 118
页数：7
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