Monotone Circuit Complexity of Matching

Bruno Cavalar; Mika Göös; Artur Riazanov; Anastasia Sofronova; Dmitry Sokolov

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arXiv · 2507.16105

Monotone Circuit Complexity of Matching

Bruno Cavalar·Mika Göös·Artur Riazanov·Anastasia Sofronova·Dmitry Sokolov

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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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Bruno Cavalar, Mika Göös, Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov. 2025-07-21. Monotone Circuit Complexity of Matching. https://arxiv.org/abs/2507.16105

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