**Conjecture**Every planar oriented graph has an acyclic induced subdigraph of order at least .

Borodin's 5-Colour Theorem states that every planar graph has an acyclic 5-colouring This implies that every planar oriented graph has an acyclic induced subdigraph of order at least .

Already improving this bound to would be interesting: it is a relaxtion of both a Conjecture of Albertson and Berman stating that every planar graph has an induced forest of order and a Conjecture of Neumann-Lara stating that every planar oriented graph can be split into two acyclic subdigraphs.

If true, this conjecture would be best possible.

## Bibliography

* indicates original appearance(s) of problem.