# Forbidden subgraphs that imply hamiltonian-connectedness

Haitze J. Broersma, Ralph J. Faudree, Andreas Huck, H. Trommel, H.J. Veldman

## 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 ${\cal L}$equation image such that if a 3‐connected graph being claw‐free and L‐free implies G is hamiltonian‐connected, then L $\in \cal L$equation image
Original language English 104-119 16 Journal of graph theory 40 2 https://doi.org/10.1002/jgt.10034 Published - 2002

## Keywords

• Hamiltonian-connected
• IR-71892
• METIS-206789
• Forbidden subgraph
• Claw-free graph