### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

- 2-factor
- Line graph
- Number of components

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

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

**The upper bound of the number of cycles in a 2-factor of a line graph.** / Fujisawa, Jun; Xiong, Liming; Yoshimoto, Kiyoshi; Zhang, Shenggui.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 55, no. 1, pp. 72-82. https://doi.org/10.1002/jgt.20220

}

TY - JOUR

T1 - The upper bound of the number of cycles in a 2-factor of a line graph

AU - Fujisawa, Jun

AU - Xiong, Liming

AU - Yoshimoto, Kiyoshi

AU - Zhang, Shenggui

PY - 2007/5

Y1 - 2007/5

N2 - 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.

AB - 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.

KW - 2-factor

KW - Line graph

KW - Number of components

UR - http://www.scopus.com/inward/record.url?scp=34248222564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248222564&partnerID=8YFLogxK

U2 - 10.1002/jgt.20220

DO - 10.1002/jgt.20220

M3 - Article

VL - 55

SP - 72

EP - 82

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -