On the number of r-transitive orientations of G(n,p)

We study the number of orientations Tr(n,p) of the binomial random graph G(n,p) in which every copy of Kr is transitive. We give the correct order of growth of log2⁡Tr(n,p) up to polylogarithmic factors. In particular, this significantly improves a result of Allen, Kohayakawa, Mota and Parente on T3(n,p).