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arXiv · 2410.05199

Counterexample to Babai's lonely colour conjecture

James Davies·Meike Hatzel·Liana Yepremyan
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Abstract

Motivated by colouring minimal Cayley graphs, in 1978, Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by constructing graphs of arbitrarily large girth and chromatic number that have a proper edge-colouring in which each cycle contains no colour exactly once.

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James Davies, Meike Hatzel, Liana Yepremyan. 2024-10-07. Counterexample to Babai's lonely colour conjecture. https://arxiv.org/abs/2410.05199

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