2 problems

Let $G$ be a connected loopless multigraph, let $\Gamma(G)$ be the corresponding metric graph with unit edge lengths, and let $r \geq 1$. For each integer $k \geq 1$, let…

Let $G$ be a connected loopless multigraph, and let $g:= |E(G)| - |V(G)| + 1$ denote its cyclomatic number. Brill–Noether gonality conjecture. Then … This is the $r=1$ case of the…