Given a directed graph $G = (V, E)$ and three vertices $u, v, w \in V$. Is it NP-Hard to find whether there is a simple path from $u$ to $v$ passing through $w$?
I found a couple of hardness statements of similar problems referring all to the same paper [The directed subgraph homeomorphism problem, Fortune, Hopcroft and Wyllie, 1980]. The papers include
- two disjoint directed paths,
- and directed simple cycle passing through two vertices.
However, it is not very clear to me, if this case reduces directly to the paper as in the case of these to problems.