Transitive triangle tilings in oriented graphs

In this paper, we prove an analogue of Corrádi and Hajnal's result. There exists n 0 such that for every n ∈ 3Z when n ≥ n 0 the following holds. If G is an oriented graph on n vertices and δ 0 (G) ≥ 7n/18, then G contains a perfect T T 3-tiling, which is a collection of vertex disjoint transitive triangles covering every vertex of G. This result is best possible, as there exists an oriented graph G on n vertices without a perfect T T 3-tiling and δ 0 (G) = ⌊7n/18⌋ − 1.