On Resolvable Multipartite G-Designs

Abstract.

A necessary and sufficient condition for the existence of a Ĉ _km −factorization of the complete symmetric k−partite multi-digraph λK*(n₁,n₂,...,n _k ) is obtained for odd k. As a consequence, a resolvable (k,n,km,λ) multipartite Ĉ _km −design exists for odd k if and only if m|n. This deduces a result of Ushio when m=1 and k=3. Further, a necessary and sufficient condition for the existence of a Ĉ _km −factorization of is established for even k, where ⊗ denotes the wreath product of graphs. Finally, a simple and short proof for the non-existence of a Ĉ _k −factorization of is obtained for odd k.