We show that if n is sufficiently large then there is a graph G of order n with In”’ log n] edges such that the transitive closure of every acyclic orientation of G has at least (,“) n3” log n edges. A consequence of this is that with Ln3’* log n] parallel processors n objects may be sorted in two time intervals. This improves considerably some results of Haggkvist and Hell. We prove similar assertions about sorting with only d-step implications.