Hamilton connectivity of line graphs and claw-free graphs

Let G be a graph and let V-0 = {v epsilon V(G): d(G)(v)= 6}. We show in this paper that: (1) if G is a 6-connected line graph and if vertical bar V-0 vertical bar <= 29 or G[V-0] contains at most 5 vertex disjoint K-4's, then G is Hamilton-connected; (ii) every 8-connected claw-free graph is Hamilton-connected. Several related results known before are generalized. (c) 2005 Wiley Periodicals, Inc.