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2011•SIAM Journal on Discrete MathematicsRequires access

Fractional colorings of cubic graphs with large girth

František Kardoš, Daniel Král͏̌, Jan Volec

Open publisher page 15 citations

Abstract

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.

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What this paper is about

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.

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OpenAlex reports 15 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Combinatorics, Mathematics, Cubic graph, Independence number, Triangle-free graph, Foster graph, Girth (graph theory), Odd graph

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