2-factors in claw-free graphs

A graph G is said to be claw-free if G has no induced subgraph isomorphic to K1,3. We study about the minimum length of cycles in 2-factors of claw-free graphs, and we show that every claw-free graph G with minimum degree δ⩾4 has a 2-factor in which each cycle contains at least ⌈δ−12⌉ vertices and every 2-connected claw-free graph G with δ⩾3 has a 2-factor in which each cycle contains at least δ vertices.