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.
|Number of pages||9|
|Journal||Journal of discrete algorithms|
|Publication status||Published - Sep 2010|
|Event||33rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2008: Mathematical Foundations of Computer Science - Torun, Poland, Torun, Poland|
Duration: 25 Aug 2008 → 29 Aug 2008
Conference number: 33