Forbidden subgraphs that imply hamiltonian-connectedness

It is proven that if G is a 3-connected claw-free graph which is also H1-free (where H1 consists of two disjoint triangles connected by an edge), then G is hamiltonian-connected. Also, examples will be described that determine a finite family of graphs ${\cal L}$ such that if a 3-connected graph being claw-free and L-free implies G is hamiltonian-connected, then L $\in \cal L$. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 104–119, 2002 The first four authors dedicate this paper to Henk Jan Veldman, a valued colleague and beloved friend who died October 12, 1998.