Let G be a graph of order n and k a positive integer. A set of subgraphs H = { H1, H2, ..., Hk } is called a k-weak cycle partition (abbreviated k-WCP) of G if H1, ..., Hk are vertex disjoint subgraphs of G such that V (G) = {n-ary union}i = 1 k V (Hi) and for all i, 1 ≤ i ≤ k, Hi is a cycle or K1 or K2. It has been shown by Enomoto and Li that if | G | = n ≥ k and if the degree sum of any pair of nonadjacent vertices is at least n - k + 1, then G has a k-WCP. We prove that if G has a k-WCP and if the minimum degree is at least (n + 2 k) / 3...
