Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k greater than or equal to 3, d greater than or equal to 4k - 1 and n greater than or equal to 3k. We show that if d(x) + d(y) greater than or equal to 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. (C) 2003 Elsevier B.V. All rights reserved.