| Abstract: | We count orientations of  avoiding certain classes of oriented graphs. In particular, we study  , the number of orientations of the binomial random graph  in which every copy of  is transitive, and  , the number of orientations of  containing no strongly connected copy of  . We give the correct order of growth of  and  up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures. |
