Gao–Ramadurai–Wanless–Wormald conjecture on rainbow matchings in multigraphs

Let $G$ be a multigraph, 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. Gao–Ramadurai–Wanless–Wormald conjecture. If $|E_i|\geq n+2$ for every $i$, then $G$ has a full rainbow matching. The conjecture is a multigraph extension of the bipartite rainbow-matching threshold and is presented as open in the source.