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Drisko \cite{drisko} proved (essentially) that every family of $2n-1$matchings of size $n$ in a bipartite graph possesses a partial rainbow matchingof size $n$. In \cite{bgs} this was generalized as follows: Any $\lfloor\frac{k+2}{k+1} n \rfloor -(k+1)$ matchings of size $n$ in a bipartite graphhave a rainbow matching of size $n-k$. We extend this latter result tomatchings of not necessarily equal cardinalities.  Settling a conjecture of Drisko, we characterize those families of $2n-2$matchings of size $n$ in a bipartite graph that do not possess a rainbowmatching of size $n$. Combining this with an idea of Alon \cite{alon}, were-prove a characterization of the extreme case in a well-known theorem ofErd\H{o}s-Ginzburg-Ziv in additive number theory.

Uniqueness of the extreme cases in theorems of Drisko and Erd\H{o}s-Ginzburg-Ziv