The firefighter number conjecture for planar graphs

Let $\mathcal{P}$ be the class of planar graphs, and let $\mathit{ff}(\mathcal{P})$ denote its firefighter number. Firefighter number conjecture for planar graphs.

$$\mathit{ff}(\mathcal{P})=2.$$

The paper notes that its proof techniques are too local to establish this claim, particularly for very large hexagonal grids, so the conjecture remains open.