Subdivisions of Transitive Tournaments

We prove that, for r ≥ 2 andn ≥ n(r), every directed graph with n vertices and more edges than the r -partite Turán graph T(r, n) contains a subdivision of the transitive tournament on r + 1 vertices. Furthermore, the extremal graphs are the orientations ofT (r, n) induced by orderings of the vertex classes.