9 problems

Brill–Noether conjecture. The gonality of a graph is bounded above by a linear function of its genus $g$.

High-order gonality conjecture. Then

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…

De Bruyn's gonality conjecture.

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…

Second gonality conjecture for generalized Crown graphs. The second gonality of the generalized Crown graph is equivalent to the paper's new upper bound.

Let $Q_n$ denote the hypercube graph of dimension $n$. The gonality and treewidth of $Q_n$ are the two graph invariants under discussion. Hypercube gap conjecture. It is conjecture…