Computing Sharp 2-Factors in Claw-Free Graphs

  • Authors:

  • Hajo Broersma;Daniël Paulusma

  • Affiliations:

  • Department of Computer Science, Durham University, Durham, United Kingdom DH1 3LE;Department of Computer Science, Durham University, Durham, United Kingdom DH1 3LE

  • Venue:
  • MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
  • Year:
  • 2008

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Abstract

In a recently submitted 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 Ryjá茂戮驴ek, Saito & Schelp.