### Abstract

Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-factor with at most 3n-2/8 components. For a simple graph with minimum degree at least three also, the same conclusion holds.

Original language | English |
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Pages (from-to) | 72-82 |

Number of pages | 11 |

Journal | Journal of Graph Theory |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 May |

### Keywords

- 2-factor
- Line graph
- Number of components

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Fujisawa, J., Xiong, L., Yoshimoto, K., & Zhang, S. (2007). The upper bound of the number of cycles in a 2-factor of a line graph.

*Journal of Graph Theory*,*55*(1), 72-82. https://doi.org/10.1002/jgt.20220