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

Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, Shenggui Zhang

Research output: Contribution to journalArticle

11 Citations (Scopus)

### 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 72-82 11 Journal of Graph Theory 55 1 https://doi.org/10.1002/jgt.20220 Published - 2007 May Yes

Line Graph
Minimum Degree
Simple Graph
Branch
Upper bound
Cycle
Odd

### Keywords

• 2-factor
• Line graph
• Number of components

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

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

In: Journal of Graph Theory, Vol. 55, No. 1, 05.2007, p. 72-82.

Research output: Contribution to journalArticle

Fujisawa, Jun ; Xiong, Liming ; Yoshimoto, Kiyoshi ; Zhang, Shenggui. / The upper bound of the number of cycles in a 2-factor of a line graph. In: Journal of Graph Theory. 2007 ; Vol. 55, No. 1. pp. 72-82.
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