Computing sharp 2-factors in claw-free graphs

Haitze J. Broersma, Daniël Paulusma

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    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 Ryj�ek, Saito and Schelp.
    Original languageEnglish
    Article number10.1016/j.jda.2009.07.001
    Pages (from-to)321-329
    Number of pages9
    JournalJournal of discrete algorithms
    Volume8
    Issue number3
    DOIs
    Publication statusPublished - Sep 2010
    Event33rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2008: Mathematical Foundations of Computer Science - Torun, Poland, Torun, Poland
    Duration: 25 Aug 200829 Aug 2008
    Conference number: 33

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