On degree sum conditions for 2-factors with a prescribed number of cycles

For a vertex subset X of a graph G, let Δt(X) be the maximum value of the degree sums of the subsets of X of size t. In this paper, we prove the following result: Let k,m be positive integers, and let G be an m-connected graph of order n≥5k−2. If Δ2(X)≥n for every independent set X of size ⌈m∕k⌉+1 in G, then G has a 2-factor with exactly k cycles. This is a common extension of the results obtained by Brandt et al. (1997) and Yamashita (2008), respectively.