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

Jun Fujisawa; Liming Xiong; Kiyoshi Yoshimoto; Shenggui Zhang

doi:10.1002/jgt.20220

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

Jun Fujisawa
, Liming Xiong
, Kiyoshi Yoshimoto
, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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	https://doi.org/10.1002/jgt.20220
State	Published - May 2007

Keywords

2-factor
Line graph
Number of components

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10.1002/jgt.20220

Cite this

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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.",

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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.

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KW - Line graph

KW - Number of components

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

Abstract

Keywords

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