Transitive triangle tilings in oriented graphs

In this paper, we prove an analogue of Corrádi and Hajnal's classical theorem. 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 every vertex has both indegree and outdegree at least 7n/18, then G contains a perfect transitive triangle tiling, which is a collection of vertex-disjoint transitive triangles covering every vertex of G. This result is best possible, as, for every n∈3Z, there exists an oriented graph G on n vertices without a perfect transitive triangle tiling in which every vertex has both indegree and outdegree at least ⌈7n/18⌉−1.