# On Fulkerson conjecture

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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Journal articles

https://hal.archives-ouvertes.fr/hal-00392009
Contributor : Jean-Marie Vanherpe <>
Submitted on : Friday, April 2, 2010 - 2:04:08 PM
Last modification on : Thursday, February 7, 2019 - 5:06:37 PM
Long-term archiving on : Friday, September 17, 2010 - 4:36:12 PM

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BergeFulkerson.pdf
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### Identifiers

• HAL Id : hal-00392009, version 2
• ARXIV : 0906.1086

### Citation

Jean-Luc Fouquet, Jean-Marie Vanherpe. On Fulkerson conjecture. Discussiones Mathematicae Graph Theory, University of Zielona Góra, 2011, 31 (2), pp.253-272. ⟨hal-00392009v2⟩

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