2 problems

The $k$-general $d$-position problem takes as input a graph $G$, integers $k\geq 2$ and $d\geq 1$, and a positive integer $r$, and asks whether $\mathrm{gp}^k_d(G)$ is greater than…

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…