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 cubic graphs. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. We give conditions for determining P1F graphs within a subfamily of generalized Petersen graphs.
Perfect one-factorizations in generalized Petersen graphs / Bonvicini, Simona; Mazzuoccolo, Giuseppe. - In: ARS COMBINATORIA. - ISSN 0381-7032. - STAMPA. - 99:(2011), pp. 33-43.
Perfect one-factorizations in generalized Petersen graphs
BONVICINI, Simona;MAZZUOCCOLO, Giuseppe
2011
Abstract
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 cubic graphs. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. We give conditions for determining P1F graphs within a subfamily of generalized Petersen graphs.
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