On the difference between hamilton cycles and 2-factors with a prescribed number of cycles

For a vertex subset X of a graph G, let Δ2(X) be the maximum degree sum of two distinct vertices of X. In this paper, we give the following result: Let k be a positive integer, 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 generalization of the results obtained by Brandt et al. [Degree conditions for 2-factors, J. Graph Theory 24 (1997), 165-173] and Yamashita [On degree sum conditions for long cycles and cycles through specified vertices, Discrete Math. 308 (2008), 6584-6587], respectively.