Formula omitted]-factors with bounded number of components in claw-free graphs

Abstract

In this paper, we show that every 3-connected claw-free graph G has a 2-factor having at most max{25(α+1),1} cycles, where α is the independence number of G. As a corollary of this result, we also prove that every 3-connected claw-free graph G has a 2-factor with at most (4|G|5(δ+2)+25) cycles, where δ is the minimum degree of G. This is an extension of a known result on the number of cycles of a 2-factor in 3-connected claw-free graphs.