Abstract: | It is shown that if G is a graph of order n with minimum degree δ(G), then for any set of k specified vertices {v1,v2,…,vk} ? V(G), there is a 2‐factor of G with precisely k cycles {C1,C2,…,Ck} such that vi ∈ V(Ci) for (1 ≤ i ≤ k) if or 3k + 1 ≤ n ≤ 4k, or 4k ≤ n ≤ 6k ? 3,δ(G) ≥ 3k ? 1 or n ≥ 6k ? 3, . Examples are described that indicate this result is sharp. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 188–198, 2003 |