We show that the perfect matching function on $n$-vertex graphs requires monotone circuits of size $\smash{2^{n^{\Omega(1)}}}$. This improves on the $n^{\Omega(\log n)}$ lower bound of Razborov (1985). Our proof uses the standard approximation method together with a new sunflower lemma for matchings.

Improvements to the presentation.

We show that the perfect matching function on $n$-vertex graphs requires monotone circuits of size $\smash{2^{n^{\Omega(1)}}}$. This improves on the $n^{\Omega(\log n)}$ lower bound of Razborov (1985). Our proof uses the standard approximation method together with a new sunflower lemma for matchings.