Article

Claw-Free Graphs and Separating Independent Sets On 2-Factors

Journal of Graph Theory
Document Type

Article
Publication Date

3-1-2012
DOI

10.1002/jgt.20579
Disciplines

Abstract

In this article, we prove that a line graph with minimum degree δ≥7 has a spanning subgraph in which every component is a clique of order at least three. This implies that if G is a line graph with δ≥7, then for any independent set S there is a 2-factor of G such that each cycle contains at most one vertex of S. This supports the conjecture that δ≥5 is sufficient to imply the existence of such a 2-factor in the larger class of claw-free graphs.
It is also shown that if G is a claw-free graph of order n and independence number α with δ≥2n/α−2 and n≥3α3/2, then for any maximum independent set S, G has a 2-factor with α cycles such that each cycle contains one vertex of S. This is in support of a conjecture that δ≥n/α≥5 is sufficient to imply the existence of a 2-factor with α cycles, each containing one vertex of a maximum independent set.
Citation Information

Ralph J. Faudree, Colton Magnant, Kenta Ozeki and Kiyoshi Yoshimoto. "Claw-Free Graphs and Separating Independent Sets On 2-Factors" *Journal of Graph Theory*Vol. 69 Iss. 3 (2012) p. 251 - 263

Available at: http://works.bepress.com/colton_magnant/31/