Directed 3-cycle decompositions of complete directed graphs with quadratic leaves

Let G be a vertex-disjoint union of directed cycles in the complete directed graph D"t, let |E(G)| be the number of directed edges of G and suppose G [email protected]?"[email protected][email protected]?"3 or [email protected]?"5 if t=5, and G [email protected]?"[email protected][email protected]?"3 if t=6. It is proved in this paper that for each positive integer t, there exist [email protected]?"3-decompositions for D"t-G if and only if t(t-1)-|E(G)|=0(mod3).