4 problems

Let $K_{m\times n}$ denote the king's graph on an $m\times n$ grid, with $4\leq m\leq n$. The gonality of a graph is denoted by $\operatorname{gon}(G)$. Eventual gonality conjectur…

Fix a positive integer $r$. For a metric graph $\Gamma=(G,l)$ with rational edge lengths, the $r^{th}$ Metric Divisorial Gonality problem asks whether…

Fix a positive integer $r$. The $r^{th}$ Stable Divisorial Gonality problem asks whether a graph has stable divisorial gonality at most a given integer. Stable divisorial gonality…

For a fixed positive integer $r$, let the $r^{th}$ Divisorial Gonality problem ask whether a graph has divisorial gonality at most a given integer, and let the $r^{th}$ Stable Divi…