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The upper bound of the number of cycles in a 2‐factor of a line graph
Author(s) -
Fujisawa Jun,
Xiong Liming,
Yoshimoto Kiyoshi,
Zhang Shenggui
Publication year - 2007
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20220
Subject(s) - combinatorics , mathematics , line graph , graph , discrete mathematics , bound graph , graph power
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 ${{3n - 2}\over {8}}$ components. For a simple graph with minimum degree at least three also, the same conclusion holds. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 72–82, 2007