Meike Hatzel, 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.

The result presented is the joint work with James Davies and Liana Yepremyan.