Perfect One-Factorizations In Generalized Petersen Graphs

Abstract

A perfectly one-factorable (PIF) 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 case in which \(G\) is a cubic graph. The existence of a PIF cubic graph is guaranteed for each admissible value of the number of vertices. We give conditions for determining PIF graphs within a subfamily of generalized Petersen graphs.