Computing sharp 2-factors in claw-free graphs

Broersma, H. J.; Paulusma, D.

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 Ryjáček, Saito & Schelp.

Citation

Broersma, H. J., & Paulusma, D. (2008, December). Computing sharp 2-factors in claw-free graphs. Presented at 33th International Symposium on Mathematical Foundations of Computer Science, Toru´n, Poland

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 33th International Symposium on Mathematical Foundations of Computer Science
• Publication Date: Jan 1, 2008
• Deposit Date: Oct 6, 2010
• Print ISSN: 0302-9743
• Publisher: Springer Verlag
• Pages: 193-204
• Series Title: Lecture notes in computer science
• Series Number: 5162
• Edition: 33th
• Book Title: Mathematical foundations of computer science 2008, 33rd International Symposium, MFCS 2008, 25-29 August 2008, Toru´n, Poland ; proceedings.
• DOI: https://doi.org/10.1007/978-3-540-85238-4_15
• Public URL: https://durham-repository.worktribe.com/output/1158525