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arXiv · 0906.1086

On Fulkerson conjecture

Jean-Luc Fouquet·Jean-Marie Vanherpe
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Abstract

If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings (a{\em Fulkerson covering}) with the property that every edge of $G$ is contained in exactly two of them. A consequence of the Fulkerson conjecture would be that every bridgeless cubic graph has 3 perfect matchings with empty intersection (this problem is known as the Fan Raspaud Conjecture). A {\em FR-triple} is a set of 3 such perfect matchings. We show here how to derive a Fulkerson covering from two FR-triples. Moreover, we give a simple proof that the Fulkerson conjecture holds true for some classes of well known snarks.

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Jean-Luc Fouquet, Jean-Marie Vanherpe. 2009-06-05. On Fulkerson conjecture. https://arxiv.org/abs/0906.1086

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