2-factors in claw-free graphs

A graph G is said to be claw-free if G has no induced subgraph isomorphic to K 1 , 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 − 1 2 ⌉ 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.