Embedding directed and undirected partial cycle systems of index λ > 1

Recent results have found small embeddings for partial m-cycle systems of order n with λ= 1. However, if λ> 1 then the best known techniques produce embeddings that are often quadratic functions of both m and n and linear functions of λ. In this article we obtain embeddings for partial m-cycle systems of order n, and of partial directed m-cycle systems, for all values of m. These embeddings are independent of λ and linear in both n and m. © 1993 John Wiley & Sons, Inc.