The problem of establishing the number of perfect matchings necessary to cover the edge-set of a cubic bridgeless graph is strictly related to a famous conjecture of Berge and Fulkerson. In thisâ€¦ (More)

A perfectly one-factorable (P1F) regular graph G is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. We consider the caseâ€¦ (More)

A one-factorization of a regular graph G is perfect if the union of any two one-factors is a Hamiltonian cycle. A graph G is said to be P1F if it possess a perfect one-factorization. We prove that Gâ€¦ (More)

A perfectly one-factorable (P1F) regular graph is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. The case of cubicâ€¦ (More)

Given a finite group G of even order, which graphs Î“ have a 1âˆ’factorization admitting G as automorphism group with a sharply transitive action on the vertex-set? Starting from this question, we proveâ€¦ (More)

In this talk we present snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided byâ€¦ (More)