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

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.

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, Shenggui Zhang
• Keywords: JGT 2007, Minimum Degree, Odd Branch-bond, Simple Graph