Theoretical computer science · Oct 6, 2026

Exponential semidefinite complexity of perfect matching

Proves that every exact semidefinite lift of the perfect matching polytope has exponential size, answering Rothvoss's polynomial-size lift question negatively. The bound holds even for the positive semidefinite rank of its odd-cut slack matrix after any fixed shift 0<ρ<10\lt \rho\lt 1, allowing arbitrary real positive semidefinite factors.

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