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

Abstract

Let G be a vertex-disjoint union of directed cycles in the complete directed graph D(t), let vertical bar E(G)vertical bar be the number of directed edges of G and suppose G not equal 54 (C) over right arrow (2) boolean OR (C) over right arrow (3) or (C) over right arrow (5) if t = 5, and G not equal (C) over right arrow (3) boolean OR (C) over right arrow (3) if t = 6. It is proved in this paper that for each positive integer t, there exist (C) over right arrow (3)-decompositions for D(t) - G if and only if t(t - 1) -vertical bar E(G)vertical bar equivalent to 0 (mod 3). (C) 2008 Elsevier B.V. All rights reserved.