Monotone Circuit Complexity of Matching

Abstract

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

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