On Fulkerson conjecture

Details On Fulkerson conjecture On Fulkerson conjecture

2009-06-05

arxiv.org/abs/0906.1086v2

Discussiones Mathematicae Graph Theory 31, 2 (2011) 253-272

Computer Science

Discrete Mathematics

Accepted for publication in Discussiones Mathematicae Graph Theory; Discussiones Mathematicae Graph Theory (2010) xxx-yyy

Scientific paper

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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