I'm looking for problems which are known to be NPC for directed graphs but has a polynomial algorithm for undirected graphs.
I've seen the question regarding the other way around here “Directed” problems that are easier than their “undirected” variant, but I'm looking for for hardness on the directed side.
For example, Feedback edge set is known to be NPC on directed but polynomial time solvable on undirected graphs.
Which other natural problems have the same property?