Orthogonal decompositions of complete digraphs

A family G of isomorphic copies of a given digraph (G) over right arrow is said to be an orthogonal decomposition of the complete digraph (D) over right arrow (n) by G if every,arc of (D) over right arrow (n) belongs to exactly one member of G and the union of any two different element's from G contains precisely one pair of reverse arcs. Given a digraph (h) over right arrow an (h) over right arrow -family in m (h) over right arrow is the vertex-disjoint union of m copies of (h) over right arrow. In this paper, we consider orthogonal decompositions by (h) over right arrow -families. Our objective is to prove the existence of such an orthogonal decomposition whenever certain. necessary conditions hold and m is sufficiently large.