On decomposing the complete symmetric digraph into orientations of K_4-e

Abstract

Let D be any of the 10 digraphs obtained by orienting the edges of K 4 − e. We establish necessary and sufficient conditions for the existence of a (K * n , D)-design for 8 of these digraphs. Partial results as well as some nonexistence results are established for the remaining 2 digraphs.