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Paper detail

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

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.

preprint2022arXivOpen access
James Davies
math.CO
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