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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1543,
author = {Jean-Luc Fouquet and Jean-Marie Vanherpe},
title = {On Fulkerson conjecture},
journal = {Discussiones Mathematicae Graph Theory},
volume = {31},
year = {2011},
pages = {253-272},
zbl = {1234.05185},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1543}
}
Jean-Luc Fouquet; Jean-Marie Vanherpe. On Fulkerson conjecture. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 253-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1543/
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