Forbidden subgraphs that imply hamiltonian‐connectedness*
Hajo J. Broersma, Ralph J. Faudree, Andreas Huck, Huib Trommel, H.J. Veldman · Journal of Graph Theory · 2002
Abstract 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