Computing sharp 2-factors in claw-free graphs |
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Authors: | Hajo Broersma Daniël Paulusma |
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Institution: | Department of Computer Science, Durham University, DH1 3LE Durham, United Kingdom |
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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 Ryjá?ek, Saito and Schelp. |
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