Disjoint triangles and quadrilaterals in a graph

Let G be a simple graph of order n and s and k be two positive integers. Brandt et al. obtained the following result: If s <= k, n >= 3s + 4(k - s) and sigma(2)(G) >= n +s, then Gcontains k disjoint cycles C-1,...,C-k satisfying vertical bar C-i vertical bar = 3 for 1 <= i <= s and vertical bar C-i vertical bar <= 4 for s < i <= k. In the above result, the length of Ci is not specified for s < i <= k. We get a result specifying the length of Ci for each s < i <= k if n >= 3s + 4(k - s) + 3. (C) 2007 Elsevier B.V. All rights reserved.