### Abstract

In this paper we give a lower bound of the circumference of a graph in terms of girth and the number of edges. It is shown that a graph of girth at least g ≥ 4 with n vertices and at least m ≥ n edges contains a cycle of length at least (g - 2)m/(n - 2). In particular, for the case g = 4, an analogous result for 2-edge-connected weighted graphs is given. Moreover, the extremal case is characterized in both results.

Original language | English |
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Pages (from-to) | 427-438 |

Number of pages | 12 |

Journal | SUT Journal of Mathematics |

Volume | 50 |

Issue number | 2 |

Publication status | Published - 2014 |

### Keywords

- Circumference
- Cycle
- Heavy cycle
- Weighted graph

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Fujisawa, J., & Ota, K. (2014). Maximal cycles in graphs of large girth.

*SUT Journal of Mathematics*,*50*(2), 427-438.