A new description of perfecly one-factorable cubic graphs

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 cubic graphs is treated. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. A description of this class was obtained by Kotzigin 1962. It is the purpose of the present paper to produce an alternative proof of Kotzig's result