For a graph G, we denote by delta(G) the minimum degree of G. A graph G is said to be claw-free if G has no induced subgraph isomorphic to K (1, 3). In this article, we prove that every claw-free graph G with minimum degree at least 4 has a 2-factor in which each cycle contains at least vertices and every 2-connected claw-free graph G with minimum degree at least 3 has a 2-factor in which each cycle contains at least delta(G) vertices. For the case where G is 2-connected, the lower bound on the length of a cycle is best possible.
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