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Conference Papers Year : 2010

Kaiser and Raspaud Conjecture on Cubic Graphs with few Vertices

Abstract

If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find $6$ perfect matchings $M_1,\ldots,M_6$ of $G$ with the property that every edge of $G$ is contained in exactly two of them and Berge conjectured that its edge set can be covered by $5$ perfect matchings. We define $\tau(G)$ as the least number of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study this parameter. The set of graphs with perfect matching index $4$ seems interesting and we give some informations on this class.
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Dates and versions

hal-00466125 , version 1 (22-03-2010)

Identifiers

  • HAL Id : hal-00466125 , version 1

Cite

Jean-Luc Fouquet, Jean-Marie Vanherpe. Kaiser and Raspaud Conjecture on Cubic Graphs with few Vertices. 17th 3in1 Workshop on Graph Theory, Nov 2008, Krynica, Poland. pp.xxx-yyy. ⟨hal-00466125⟩
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