Delcourt–Postle conjecture on full rainbow matchings in multigraphs

Let $G$ be a multigraph with maximum degree $\Delta$, and let $E_1,\ldots,E_n$ be color classes of a proper edge-coloring of $G$. A full rainbow matching is a matching containing exactly one edge from each color class. Delcourt–Postle conjecture. If $|E_i|\geq \Delta+2$ for every $i$, then $G$ has a full rainbow matching. The source later states that both this conjecture and the preceding bipartite conjecture are false, even when the chromatic index equals the maximum degree; consequently this conjecture is refuted.