Download PDF - On Fulkerson conjecture
ArticleOriginal scientific text
Title
On Fulkerson conjecture
Authors 1, 1
Affiliations
- 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
Bibliography
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Pages:
253-272
Main language of publication
English
Received
2009-12-08
Accepted
2010-04-02
Published
2011
DOI: 10.7151/dmgt.1543
Exact and natural sciences