Baker's subdivision and metric-graph gonality conjecture

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 $\sigma_k(G)$ denote the multigraph obtained by subdividing every edge of $G$ into $k$ parts. Baker's gonality conjecture. Then:

(a)

$$\operatorname{dgon}_{r}(G) = \operatorname{dgon}_{r}(\sigma_k(G))$$

for all $k \geq 1$; and

(b)

$$\operatorname{dgon}_{r}(\Gamma(G)) = \operatorname{dgon}_{r}(G).$$

This was posed as the second remaining conjecture in Baker's work on divisors on graphs. The paper's abstract states that it settles this conjecture in the negative by exhibiting graphs whose metric divisorial gonality is strictly smaller than their discrete divisorial gonality, so the conjecture is refuted.