# 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

### Cite this

Broersma, Haitze J. ; Paulusma, Daniël ; Yoshimoto, Kiyoshi. / Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs. In: Graphs and combinatorics. 2009 ; Vol. 25, No. 4. pp. 427-460.
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Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs. / Broersma, Haitze J.; Paulusma, Daniël; Yoshimoto, Kiyoshi.

In: Graphs and combinatorics, Vol. 25, No. 4, 10.1007/s00373-009-0855-7, 2009, p. 427-460.

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T1 - Sharp upper bounds on the minimum number of components of 2-factors in claw-free graphs

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AU - Yoshimoto, Kiyoshi

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N2 - 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.

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