The feedback vertex set bound for planar graphs of prescribed girth

Let $G$ be a finite simple planar graph of size $m$ and girth $g$, where the girth is the length of a shortest cycle. A feedback vertex set is a set of vertices whose removal leaves an acyclic graph.

Feedback vertex set conjecture for prescribed girth. There exists a feedback vertex set $S$ of $G$ satisfying

$$|S| \le \frac{m}{g}.$$

Equivalently, $G$ has an induced forest with at least $|V(G)|-\frac{m}{g}$ vertices. The source presents this as a conjecture for planar graphs with given girth and provides no evidence of resolution.