 |
|
|
|
| HAL : hal-00392009, version 2 |
| arXiv : 0906.1086 |
| Fiche détaillée |  Récupérer au format |
|
|
| Discussiones Mathematicae Graph Theory 31, 2 (2011) 253-272 |
|
|
| Versions disponibles : | v1 (05-06-2009) | v2 (31-05-2010) |
|
|
|
|
| On Fulkerson conjecture |
|
|
| Jean-Luc Fouquet 1Jean-Marie Vanherpe 1 |
|
|
| (2011) |
|
|
|
| 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. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire d'Informatique Fondamentale d'Orléans (LIFO) |
|
|
|
Université d'Orléans : EA4022 – Ecole Nationale Supérieure d'Ingénieurs de Bourges |
|
|
|
|
|
|
|
|
|
| Domaine | : | Informatique/Mathématique discrète |
|
|
| Cubic graphs – perfect matchings |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00392009, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00392009 | |
| oai:hal.archives-ouvertes.fr:hal-00392009 | |
| Contributeur : Jean-Marie Vanherpe | |
| Soumis le : Vendredi 2 Avril 2010, 14:04:08 | |
| Dernière modification le : Jeudi 31 Mars 2011, 15:41:44 | |
