6 problems

Develin–Hartke conjecture. There exists an outbreak on $\mathbb{Z}^d$ which cannot be contained by deploying $f(n)$ firefighters at time $n$.

The strong grid is the graph obtained from the square grid by joining vertices that are at king-move distance one, so each vertex is adjacent also to its diagonal neighbours. In th…

Consider the Pyro game on the infinite Cartesian grid, with the original burned vertex at $(0,0)$ and one firefighter protecting vertices over successive steps. Here, a vertex's di…

Develin–Hartke conjecture. There exists an outbreak on $\mathbb{L}^d$ that cannot be contained by deploying $f(t)$ firefighters at time $t$.

Let $\mathcal{P}_5$ be the class of planar graphs of girth at least $5$, and let $\mathit{ff}(\mathcal{P}_5)$ denote its firefighter number. Firefighter number conjecture for plana…

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. … The paper note…