Expected-gonality conjecture for smooth tropical plane curves

Let $P$ be a lattice polygon and let $\Gamma$ be a smooth tropical plane curve with Newton polygon $P$. The expected-gonality conjecture asserts that

$$\operatorname{gon}(\Gamma)=\operatorname{egon}(P).$$

Here $\operatorname{gon}(\Gamma)$ is the divisorial gonality of the tropical curve, and $\operatorname{egon}(P)$ is the expected gonality, a quantity derived from the lattice width of $P$.

The conjecture extends the relationship between the gonality of an algebraic curve and its Newton polygon to tropical curves. It holds trivially for polygons of genus $0$ or $1$ and is known for hyperelliptic tropical curves, but remains open in general.