We consider the complexity of the firefighter problem where ${b \geq 1}$ firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al. 2007) and on trees of bounded degree $b+3$ for any fixed budget ... more >>>

Recently, perfect matching in bounded planar cutwidth bipartite graphs
$BGGM$ was shown to be in ACC$^0$ by Hansen et al.. They also conjectured that
the problem is in AC$^0$.
In this paper, we disprove their conjecture by showing that the problem is
not in AC$^0[p^{\alpha}]$ for every prime $p$. ... more >>>