Triangle-free graphs with large chromatic number and no induced wheel
Combinatorics
2022-02-18 v3
Abstract
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.
Cite
@article{arxiv.2104.05907,
title = {Triangle-free graphs with large chromatic number and no induced wheel},
author = {James Davies},
journal= {arXiv preprint arXiv:2104.05907},
year = {2022}
}