22-factors with bounded number of components in claw-free graphs

In this paper, we show that every 33-connected claw-free graph GG has a 22-factor having at most max{25(α+1),1} cycles, where αα is the independence number of GG. As a corollary of this result, we also prove that every 33-connected claw-free graph GG has a 22-factor with at most (4|G|5(δ+2)+25) cycles, where δδ is the minimum degree of GG. This is an extension of a known result on the number of cycles of a 22-factor in 33-connected claw-free graphs.