4 problems

Let $P^{\Box,n}_\infty$ be the $n$-dimensional infinite grid, and let $\mathrm{gp}^k(G)$ denote its $k$-general position number. Infinite-grid conjecture. … This conjecture is moti…

Let $K$ denote the infinite king grid, and let $\operatorname{DET:LD}(K)$ denote its deterministic locating-dominating density. Deterministic locating-dominating density conjecture…

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…

Let the infinite Cartesian grid be the graph whose vertices are the integer lattice points and whose edges join lattice points at grid distance one. In the firefighter model, firef…