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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机译：令$ G $为无爪图，阶次为$ n $，最小度为$ \ delta $。我们改善了Faudree等人的结果。和Gould＆Jacobson，并通过证明以下两个结果来解决两个未解决的问题。如果$ \ delta = 4 $，则$ G $具有最多包含$（5n-14）/ 18 $分量的2因子，除非$ G $属于有限类的例外图。如果$ \ delts \ ge 5 $，则$ G $具有最多包含$（n-3）/（\ delta-1）$分量的2因子，除非$ G $是完整的图。在我们不能用较小的商代替5/18并且不能分别用$ \ delta $代替$ \ delta-1 $的意义上，这些界限是最好的。
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