Weak Jackson–Thomassen orientation conjecture

A digraph $D$ is $k$-strong if it has at least $k+1$ vertices and remains strongly connected after the deletion of any set of at most $k-1$ vertices. An orientation of a digraph is an oriented spanning subdigraph obtained by deleting precisely one arc from every directed 2-cycle. Weak Jackson–Thomassen conjecture. There exists a function $f(k)$ so that every $f(k)$-strong digraph on at least $2k+1$ vertices contains a spanning $k$-strong oriented graph. This natural weakening is open for general digraphs already when $k=2$, although it holds for symmetric digraphs for all $k$.