Harutyunyan's acyclic-set conjecture for planar oriented graphs

Let an oriented graph be a digraph without loops and multiple arcs, and let an acyclic set be a set of vertices inducing a subgraph with no directed cycles. Harutyunyan's conjecture. Every planar oriented graph of order $n$ has an acyclic set of size at least $\frac{3n}{5}$. The conjecture is refuted by the paper's construction of oriented planar graphs whose maximum acyclic set has size at most $\lceil \frac{n+1}{2} \rceil$.