New bound shows perfect matching needs monotone circuits of size 2^{n^{Ω(1)}} in n-vertex graphs, indicating significant complexity.
We show that the perfect matching function on n-vertex graphs requires monotone circuits of size 2^nΩ(1). This improves on the nΩ(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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Cavalar et al. (2025) studied this question.
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