Monotone Circuit Complexity of Matching

Published 21 Jul 2025 in cs.CC and math.CO | (2507.16105v1)

Abstract: 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.

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