## Abstract

In the first one in this series of two papers, we have proved that every 3-connected (Formula presented.) -free graph is Hamilton-connected. In this paper, we continue in this direction by proving that every 3-connected (Formula presented.) -free graph, where (Formula presented.), is Hamilton-connected (where (Formula presented.) is the graph obtained by attaching endvertices of three paths of lengths (Formula presented.) to a triangle). This together with a previous result of other authors completes the characterization of forbidden induced generalized nets implying Hamilton-connectedness of a 3-connected claw-free graph. We also discuss remaining open cases in a full characterization of connected graphs (Formula presented.) such that every 3-connected (Formula presented.) -free graph is Hamilton-connected.

Original language | English |
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Pages (from-to) | 119-138 |

Number of pages | 20 |

Journal | Journal of Graph Theory |

Volume | 103 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2023 |

## Keywords

- claw-free
- closure
- forbidden subgraph
- hamilton-connected
- net-free