Broersma, H.J. and Paulusma, Daniel (2010) 'Computing sharp 2-factors in claw-free graphs.', Journal of discrete algorithms., 8 (3). pp. 321-329.
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.
|Keywords:||Claw-free graph, 2-factor, Number of components, Polynomial algorithm.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.jda.2009.07.001|
|Publisher statement:||NOTICE: this is the author's version of a work that was accepted for publication in Journal of discrete algorithms.|
|Date accepted:||No date available|
|Date deposited:||07 October 2010|
|Date of first online publication:||September 2010|
|Date first made open access:||No date available|
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