Counterexample to Babai's lonely colour conjecture
<|reference_start|>Counterexample to Babai's lonely colour conjecture: 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.<|reference_end|>
@article{davies2024counterexample,
    title={Counterexample to Babai's lonely colour conjecture},
    author={James Davies and Meike Hatzel and Liana Yepremyan},
    journal={arXiv preprint arXiv:2410.05199},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.05199},
    primaryClass={math.CO cs.DM math.GR}
}