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17516 Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs

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Broersma, H.J. and Paulusma, D. and Yoshimoto, K. (2009) Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs. Graphs and Combinatorics, 25 (4). pp. 427-460. ISSN 0911-0119 *** ISI Impact 0,571 ***

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Official URL: http://dx.doi.org/10.1007/s00373-009-0855-7

Abstract

Let $G$ be a claw-free graph with order $n$ and minimum degree $\delta$ . We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If $\delta = 4$ , then $G$ has a 2-factor with at most $(5n - 14)/ 18$ components, unless $G$ belongs to a finite class of exceptional graphs. If $\delts \ge 5$ , then $G$ has a 2-factor with at most $(n - 3)/(\delta - 1)$ components, unless $G$ is a complete graph. These bounds are best possible in the sense that we cannot replace 5/18 by a smaller quotient and we cannot replace $\delta - 1$ by $\delta$ , respectively.

Item Type:	Article
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
ID Code:	17516
Status:	Published
Deposited On:	18 February 2010
Refereed:	Yes
International:	Yes
ISI Impact Factor:	0,571
More Information:	statistics metis

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