Fractional colorings of cubic graphs with large girth
František Kardoš, Daniel Král͏̌, Jan Volec · SIAM Journal on Discrete Mathematics · 2011
We show that every (sub)cubic [Formula: see text]-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978, which implies that it contains an independent set of size at least [Formula: see text]. Our bound on the independence number is valid for random cubic graphs as well, as it improves existing lower bounds on the maximum cut in cubic graphs with large girth.