Covering vertices of a graph by k disjoint cycles Original Research Article

Let d, k and n be three integers with k⩾3, d⩾4k−1 and n⩾3k. We show that if d(x)+d(y)⩾d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.