Baker's Brill-Noether existence conjecture for finite graphs

Let $G$ be a finite, undirected, connected, loop-free multigraph of genus $g$. Define the Brill-Noether number by

$$\rho(g,r,d)=g-(r+1)(g-d+r).$$

A divisor on $G$ has a degree and a rank in the usual graph-theoretic sense. Brill-Noether existence conjecture for graphs. For every pair of non-negative integers $r_0,d_0$ satisfying $\rho(g,r_0,d_0)\geq 0$, there is a divisor $D$ on $G$ of degree $d_0$ and rank at least $r_0$; equivalently, there is a divisor of degree at most $d_0$ and rank equal to $r_0$.

This is the graph-theoretic analogue of the existence part of the classical Brill-Noether theorem. The paper identifies this conjecture as its principal focus; its resolution status is not specified in the supplied material.