On the doyen‐wilson theorem for m‐cycle systems

In this article we consider the embedding of m ‐cycle systems of order u in m ‐cycle systems of order v when m is odd. When u and v are 1 or m (mod 2 m ) we completely settle this problem, except possibly for the smallest such embedding in some cases when u ≡ v ≡ m (mod 2 m ). In particular, there are no exceptions if m ∈ {7,9}, so the generalization of the Doyen‐Wilson Theorem is now settled for all odd m with m ≤ 9. © 1994 John Wiley & Sons, Inc.