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

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