Circumferences of 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. Matthews and Sumner [J. Graph Theory 9 (1985), no. 2, 269–277] proved that if G is a 2-connected claw-free graph of order n, then c(G) ≥ min{2δ(G) + 4, n}, where let δ(G) and c(G) denote the minimum degree and the length of a longest cycle of G, respectively. In this paper, we generalize this result as follows: if G is a 2-connected claw-free graph of order n with δ(G) ≥ 7, then G has a 2-factor F such that c(F ) ≥ min{2δ(G) + 4, n}.