### Abstract

It is proven that if $G$ is a $3$-connected claw-free graph which is also $Z_3$-free (where $Z_3$ is a triangle with a path of length $3$ attached), $P_6$-free (where $P_6$ is a path with $6$ vertices) or $H_1$-free (where $H_1$ 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 $L\in\cal{L}$.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1999 |

### Publication series

Name | Memorandum / Faculty of Mathematical Sciences |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1481 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C45
- MSC-05C35
- EWI-3301
- IR-65670
- MSC-05C38

## Cite this

Broersma, H. J., Faudree, R. J., Huck, A., Trommel, H., & Veldman, H. J. (1999).

*Forbidden subgraphs that imply Hamiltonian-connectedness*. (Memorandum / Faculty of Mathematical Sciences; No. 1481). Enschede: University of Twente, Department of Applied Mathematics.