On the number of components in 2-factors of claw-free graphs

In this paper, we prove that if a claw-free graph G with minimum degree δ ⩾ 4 has no maximal clique of two vertices, then G has a 2-factor with at most ( | G | - 1 ) / 4 components. This upper bound is best possible. Additionally, we give a family of claw-free graphs with minimum degree δ ⩾ 4 in whi...

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Bibliographic Details
Published inDiscrete mathematics Vol. 307; no. 22; pp. 2808 - 2819
Main Author Yoshimoto, Kiyoshi
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.10.2007
Elsevier
Subjects
2-Factor
Algebra
Claw-free graphs
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Line graphs
Mathematics
Sciences and techniques of general use
Line graphs
Claw-free graphs
2-Factor
Upper bound
Line graph
Discrete mathematics
Claw free graph
Combinatorics
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Summary:In this paper, we prove that if a claw-free graph G with minimum degree δ ⩾ 4 has no maximal clique of two vertices, then G has a 2-factor with at most ( | G | - 1 ) / 4 components. This upper bound is best possible. Additionally, we give a family of claw-free graphs with minimum degree δ ⩾ 4 in which every 2-factor contains more than n / δ components.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2006.11.022