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 Kotzig in 1962. It is the purpose of the present paper to produce an alternative proof of Kotzig’s result.
A new description of perfectly one-factorable cubic graphs
Mazzuoccolo, Giuseppe
2006-01-01
Abstract
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 Kotzig in 1962. It is the purpose of the present paper to produce an alternative proof of Kotzig’s result.
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