Pentagons and cycle coverings

Let G be a graph of order n ≥ 5k + 2, where k is a positive integer. Suppose that the minimum degree of G is at least (n + k)/2 . We show that G contains k pentagons and a path such that they are vertexdisjoint and cover all the vertices of G. Moreover, if n ≥ 5k + 7, then G contains k + 1 vertex-disjoint cycles covering all the vertices of G such that k of them are pentagons. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 194–208, 2007