### 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 |
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Pages (from-to) | 104-119 |

Number of pages | 16 |

Journal | Journal of graph theory |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 |

### Keywords

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

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## Cite this

Broersma, H. J., Faudree, R. J., Huck, A., Trommel, H., & Veldman, H. J. (2002). Forbidden subgraphs that imply hamiltonian-connectedness.

*Journal of graph theory*,*40*(2), 104-119. https://doi.org/10.1002/jgt.10034