Vertex‐disjoint cycles of length at most four each of which contains a specified vertex*

We obtain a sharp minimum degree condition δ (G) ≥ of a graph G of order n ≥ 3k guaranteeing that, for any k distinct vertices, G contains k vertex‐disjoint cycles of length at most four each of which contains one of the k prescribed vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 37–47, 2001