Computing sharp 2-factors in claw-free graphs

  • Authors:

  • Hajo Broersma;Daniël Paulusma

  • Affiliations:

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

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

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 Ryjacek, Saito and Schelp.