## Abstract

A graph G is said to be pancyclic if G contains cycles of lengths from 3 to |V(G)|. For a positive integer i, we use Z_{i} to denote the graph obtained by identifying an endpoint of the path P_{i} _{+} _{1} with a vertex of a triangle. In this paper, we show that every 4-connected claw-free Z_{8}-free graph is either pancyclic or is the line graph of the Petersen graph. This implies that every 4-connected claw-free Z_{6}-free graph is pancyclic, and every 5-connected claw-free Z_{8}-free graph is pancyclic.

Original language | English (US) |
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Pages (from-to) | 67-89 |

Number of pages | 23 |

Journal | Graphs and Combinatorics |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2 2019 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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