On the number of components in 2-factors of claw-free graphs

In this paper, we prove that if a claw-free graph G   with minimum degree δ⩾4δ⩾4 has no maximal clique of two vertices, then G   has a 2-factor with at most (|G|-1)/4(|G|-1)/4 components. This upper bound is best possible. Additionally, we give a family of claw-free graphs with minimum degree δ⩾4δ⩾4 in which every 2-factor contains more than n/δn/δ components.