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. - In: TEH AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 1034-4942. - 41(2008), pp. 227-233.
Titolo: | Perfect one-factorizations in line-graphs and planar graphs |
Autori: | |
Data di pubblicazione: | 2008 |
Rivista: | |
Citazione: | Perfect one-factorizations in line-graphs and planar graphs / Mazzuoccolo, Giuseppe. - In: TEH AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 1034-4942. - 41(2008), pp. 227-233. |
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. |
Handle: | http://hdl.handle.net/11562/927933 |
Appare nelle tipologie: | 01.01 Articolo in Rivista |
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