  If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find 6
perfect matchings $M_1,...,M_6$ 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.
