  We give here new upper bounds on the size of a smallest feedback vertex set
in planar graphs with high girth. In particular, we prove that a planar graph
with girth $g$ and size $m$ has a feedback vertex set of size at most
$\frac{4m}{3g}$, improving the trivial bound of $\frac{2m}{g}$. We also prove
that every $2$-connected graph with maximum degree $3$ and order $n$ has a
feedback vertex set of size at most $\frac{n+2}{3}$.
