Partition of a graph into cycles and vertices Original Research Article

Let G be a graph of order n and k a positive integer. A set of subgraphs image is called a k-weak cycle partition (abbreviated k-WCP) of G if image are vertex disjoint subgraphs of G such that image and for all i, image, image is a cycle or image or image. It has been shown by Enomoto and Li that if image and if the degree sum of any pair of nonadjacent vertices is at least image, then G has a k-WCP. We prove that if G has a k-WCP and if the minimum degree is at least image, then G can be partitioned into k subgraphs image, image, where each image is a cycle or image.