### Abstract

We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{d_{G}(u) + d_{G}(v)|d_{G}(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ(G) - 1}.

Original language | English |
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Pages (from-to) | 275-279 |

Number of pages | 5 |

Journal | Journal of Graph Theory |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1997 Mar |

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Enomoto, H., Hirohata, K., & Ota, K. (1997). Long Cycles Passing Through a Specified Edge in a 3-Connected Graph.

*Journal of Graph Theory*,*24*(3), 275-279. https://doi.org/10.1002/(SICI)1097-0118(199703)24:3<275::AID-JGT9>3.0.CO;2-M