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 [M.M. Matthews, D.P. Sumner, Longest paths and cycles in K1,3-free graphs, J. Graph Theory 9 (1985) 269-277] proved that c(G)≥min{2δ(G)+4,n} if G is a 2-connected claw-free graph of order n, where for a graph G, let δ(G) and c(G) denote the minimum degree and the length of a longest cycle of G, respectively. In this paper, we extend this result for a graph G with δ(G)≥7 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}.