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

We obtain a sharp minimum degree condition δ (G) ≥  $\lfloor {\sqrt {\phantom{n^2}n+k^2-3k+1}}\rfloor + 2k-1$ of a graph G of order n  ≥ 3 k 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