Transitive triangle tilings in oriented graphs

In this paper, we prove an analogue of Corr´adi and Hajnal’s classical theorem. There exists n0 such that for every n ∈ 3Z when n ≥ n0 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 vertexdisjoint 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.