A claw-free graph is a graph that does not contain \(K_{1,3}\) as an induced subgraph, and a 2-factor of a graph is a 2-regular spanning subgraph. In 1997, Ryjáček introduced the closure concept of claw-free graphs, and Hamilton cycles and related structures in claw-free graphs have been intensively studied via the closure concept. In this paper, using the closure concept, we show that for a claw-free graph G of order n, if every independent set I of G satisfies \(|I|\le \delta _G(I)-1\) and G satisfies \(\sigma _k(G)\ge n\) , then G has a 2-factor with at most \(k-1\) cycles, where \(\delta _G(I)\) denotes the minimum degree of the vertices in I. As a corollary of the result, we show that every claw-free graph G with \(\delta (G)\ge \alpha (G)+1\) has a 2-factor with at most \(\alpha (G)\) cycles, which partially solves a conjecture by Faudree et al. in 2012. Furthermore, we show some results on 2-factors and degenerate cycle partitions of a claw-free graph G with \(\sigma _k(G)\ge n\) .
