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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

Provided by:
Durham Research Online

Downloaded from
http://dro.dur.ac.uk/7418/1/7418.pdf

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