Grinblat's rainbow matching conjecture

A rainbow matching is a matching whose edges have pairwise distinct colors. Grinblat's conjecture. If $G$ is a multigraph that is not necessarily properly edge colored with $n$ colors, each color class being the disjoint union of non-trivial cliques and spanning at least $3n-2$ vertices, then $G$ has a rainbow matching of size $n$. The conjecture was fully proved by Munhá Correia and Sudakov.