5 problems

Let $\operatorname{Qd}(m,n,r)$ denote the toroidal grid obtained from a grid of meridian length $m$ and longitude length $n$, with a shift by $r$ when traversing the meridian. A gr…

Let $n,m \geq 3$ with $(n,m) \neq (4,4)$. A toroidal $(n,m)$-grid is the toroidal grid with parameters $n$ and $m$, and periodic means periodic under the discrete-time quantum walk…

Let $C_n$ and $C_m$ be odd cycles, so that $C_n\Box C_m$ is an odd-by-odd toroidal grid. Its Alon–Tarsi number is $4$, while the list chromatic number $\chi_l(G)$ is the least inte…

Let $T_{m,n}=C_m\Box C_n$ be the toroidal grid with $m,n\geq 3$, where $C_m$ and $C_n$ are cycles. An assignment of finite color lists to the vertices is a list assignment, and…

Let $t_n$ denote the relevant capture-time quantity for the toroidal grid of side length $n$, and let $z(T_n)$ denote the minimum number of zombies needed to catch the survivor on…