Computing sharp 2-factors in claw-free graphs


Broersma, H.J. and Paulusma, D. (2008) Computing sharp 2-factors in claw-free graphs. In: 33rd International Symposium on Mathematical Foundations of Computer Science, August 27-31, 2008, Torun, Poland (pp. pp. 193-204).

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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 Ryjáček, Saito & Schelp.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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