Kowalik et al.'s conjecture on induced forests in planar graphs of girth at least five

Let $G$ be a finite simple planar graph of order $n$ and girth at least $5$, where the girth is the length of a shortest cycle.

Kowalik et al.'s conjecture. The graph $G$ admits an induced forest of order at least

$$\frac{7n}{10}.$$

This conjecture seeks a stronger induced-forest bound for planar graphs excluding short cycles. The source describes a companion result as a first step toward the conjecture, but does not state that the conjecture has been resolved.