Counterexample to Babai's lonely colour conjecture
Combinatorics
2024-10-08 v1 Discrete Mathematics
Group Theory
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.
Cite
@article{arxiv.2410.05199,
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}
}
Comments
11 pages, 3 figures