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| HAL: hal-00392009, version 2 |
| arXiv: 0906.1086 |
| Detailed view |  Export this paper |
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| Discussiones Mathematicae Graph Theory 31, 2 (2011) 253-272 |
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| Available versions: | v1 (2009-06-05) | v2 (2010-05-31) |
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| On Fulkerson conjecture |
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| Jean-Luc Fouquet 1Jean-Marie Vanherpe 1 |
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| (2011) |
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| 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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| 1: | Laboratoire d'Informatique Fondamentale d'Orléans (LIFO) |
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Université d'Orléans : EA4022 – Ecole Nationale Supérieure d'Ingénieurs de Bourges |
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| Subject | : | Computer Science/Discrete Mathematics |
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| Cubic graphs – perfect matchings |
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| hal-00392009, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00392009 | |
| oai:hal.archives-ouvertes.fr:hal-00392009 | |
| From: Jean-Marie Vanherpe | |
| Submitted on: Friday, 2 April 2010 14:04:08 | |
| Updated on: Thursday, 31 March 2011 15:41:44 | |
