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Computing sharp 2-factors in claw-free graphs.\ud

By H.J. Broersma and Daniel Paulusma

Abstract

In a previous paper we obtained an upper bound for the minimum number of components of a 2-factor in a claw-free graph. This bound is sharp in the sense that there exist infinitely many claw-free graphs for which the bound is tight. In this paper we extend these results by presenting a polynomial algorithm that constructs a 2-factor of a claw-free graph with minimum degree at least four whose number of components meets this bound. As a byproduct we show that the problem of obtaining a minimum 2-factor (if it exists) is polynomially solvable for a subclass of claw-free graphs. As another byproduct we give a short constructive proof for a result of Ryjáček, Saito and Schelp.\ud \u

Topics: Claw-free graph, 2-factor, Number of components, Polynomial algorithm.
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.jda.2009.07.001
OAI identifier: oai:dro.dur.ac.uk.OAI2:7418
Journal:

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