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A classical result of Erd\H{o}s and Gallai determines the maximum size$m(n,\nu)$ of a graph $G$ of order $n$ and matching number $\nu n$. We showthat $G$ has factorially many maximum matchings provided that its size issufficiently close to $m(n,\nu)$.

Factorially many maximum matchings close to the Erd\H{o}s-Gallai bound