In this article, we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been defined by the first author (On a closure concept in claw-free graphs, J Combin Theory Ser B 70 (1997), 217-224). For a claw-free graph G and its closure cl(G), We prove: (1) V (G) is covered by #kappa# cycles in G if and only if V (cl(G)) is covered by #kappa# cycles of cl(G); and (2) G has a 2-factor with at most #kappa# components if and only if cl(G) has a 2-factor with at most #kappa# components.
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机译：在本文中，我们研究了无爪图及其闭合的2个因数的周期覆盖率和2个因子的影响，该周期覆盖率和闭合率由第一作者定义（关于无爪图的闭合概念，J Combin Theory Ser B 70（ 1997），217-224）。对于无爪图G及其闭合cl（G），我们证明：（1）当且仅当V（cl（G））被#kappa覆盖时，V（G）被G中的＃kapp＃个环覆盖。 cl（G）个循环; （2）当且仅当cl（G）具有最多＃kappa＃个成分的2因子时，G才具有最多＃kapp＃个成分的2因子。
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