Discussiones Mathematicae Graph Theory 31(2) (2011) 253-272
doi: 10.7151/dmgt.1543

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ON FULKERSON CONJECTURE

Jean-Luc Fouquet  and  Jean-Marie Vanherpe

L.I.F.O., Faculté des Sciences, B.P. 6759
Université d'Orléans
45067 Orléans Cedex 2, France

Abstract

If G is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings (a 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 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.

Keywords: cubic graph, perfect matchings.

2010 Mathematics Subject Classification: 05C15, 05C70.

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Received 8 December 2009
Revised 2 April 2010
Accepted 6 April 2010