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

Haitze J. Broersma, Daniël Paulusma, Kiyoshi Yoshimoto

6 Citations (Scopus)

## 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.
Original language Undefined 10.1007/s00373-009-0855-7 427-460 34 Graphs and combinatorics 25 4 https://doi.org/10.1007/s00373-009-0855-7 Published - 2009

• EWI-17516
• IR-70041
• METIS-265816