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 G is a P1F cubic graph if and only if L(G) is a P1F quartic graph. Moreover, we give some necessary conditions for the existence of a P1F planar graph.
Perfect one-factorizations in line-graphs and planar graphs
Mazzuoccolo, Giuseppe
2008-01-01
Abstract
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 G is a P1F cubic graph if and only if L(G) is a P1F quartic graph. Moreover, we give some necessary conditions for the existence of a P1F planar graph.
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