Asymptotic results on suborthogonal [formula omitted]-decompositions of complete digraphs

Abstract

A G → -decomposition of a complete digraph D → n is a partition of D → n into isomorphic copies (called pages) of G → . A G → -decomposition is said to be suborthogonal if the union of any two distinct pages contains at most one pair of reverse arcs. Wilson (Proceedings of the fifth British Combinatorial Conference, 1975, pp. 647–659) proved in 1975 that a G → -decomposition exists for almost all integers n satisfying certain necessary conditions. In this paper we shall prove that under the same conditions there exists even a suborthogonal G → -decomposition.