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.

翻译：受极小凯莱图着色问题的启发，巴拜于1978年提出猜想：无孤独着色图的色数存在上界。我们通过构造一类具有任意大围长和色数的图，强有力地否定了该猜想——这类图存在真边着色方案，使得其中任意环均不包含恰好出现一次的色边。