The elementary multigraph reformulation of the Goldberg–Seymour conjecture

Let $G=(V,E)$ be a multigraph. Define its density by

$$\Gamma(G)=\max\left\{\frac{2|E(U)|}{|U|-1}:U\subseteq V,\ |U|\geq 3\text{ and odd}\right\},$$

and call $G$ elementary when $\chi'(G)=\lceil\Gamma(G)\rceil$.

Elementary-multigraph conjecture. Every multigraph $G$ with

$$\chi'(G)\geq\Delta(G)+2$$

is elementary.

The source presents this as a reformulation of the Goldberg–Seymour conjecture, which was proved in the paper; hence this formulation is solved as well.