Orthogonal Decompositions of Complete Digraphs

Abstract.

 A family ? of isomorphic copies of a given digraph is said to be an orthogonal decomposition of the complete digraph by , if every arc of belongs to exactly one member of ? and the union of any two different elements from ? contains precisely one pair of reverse arcs.

Given a digraph , an -family is the vertex-disjoint union of m copies of . In this paper, we consider orthogonal decompositions by -families. Our objective is to prove the existence of such an orthogonal decomposition whenever certain necessary conditions hold and m is sufficiently large.