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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.
[1] Jean-Marie Vanherpe,et al. On Fan Raspaud Conjecture , 2008, ArXiv.
[2] J. A. Bondy,et al. Graph Theory with Applications , 1978 .
[3] Daniel Král,et al. Unions of perfect matchings in cubic graphs , 2005, Electron. Notes Discret. Math..
[4] D. R. Fulkerson,et al. Blocking and anti-blocking pairs of polyhedra , 1971, Math. Program..
[5] André Raspaud,et al. Fulkerson's Conjecture and Circuit Covers , 1994, J. Comb. Theory, Ser. B.