The Tur\'an Number of Surfaces
Abstract
We show that there is a constant c such that any 3-uniform hypergraph H with n vertices and at least cn5/2 edges contains a triangulation of the real projective plane as a subgraph. This resolves a conjecture of Kupavskii, Polyanskii, Tomon, and Zakharov. Furthermore, our work, combined with prior results, asymptotically determines the Tur\'an number of all surfaces.
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