### Abstract

Let cl(G) denote Ryjáček's closure of a claw-free graph G. In this article, we prove the following result. Let G be a 4-connected claw-free graph. Assume that G[N _{G}(T)] is cyclically 3-connected if T is a maximal K _{3} in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267-276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262-272].

Original language | English |
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Pages (from-to) | 40-53 |

Number of pages | 14 |

Journal | Journal of Graph Theory |

Volume | 70 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 May 1 |

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### Keywords

- Hamiltonian cycle
- claw-free graph
- maximal K

### ASJC Scopus subject areas

- Geometry and Topology