3 problems

Let $P_n$ denote the finite path grid used to form the three-dimensional grid $P_n\times P_n\times P_n$. Consider an outbreak beginning at one vertex, with one firefighter deployed…

Let $\mathbb{L}^{d}$ be the infinite $d$-dimensional square grid, whose vertices are the points of $\mathbb{R}^{d}$ with integer coordinates, with adjacency defined by Euclidean di…

Let $\mathbb{L}^{d}$ be the infinite $d$-dimensional square grid, whose vertices are the points of $\mathbb{R}^{d}$ with integer coordinates, with adjacency defined by Euclidean di…