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Pré-Publication, Document De Travail Année : 2021

The extremal number of surfaces

Andrey Kupavskii
Alexandr Polyanskii
  • Fonction : Auteur
István Tomon
  • Fonction : Auteur
Dmitriy Zakharov
  • Fonction : Auteur

Résumé

In 1973, Brown, Erd\H{o}s and S\'os proved that if $\mathcal{H}$ is a 3-uniform hypergraph on $n$ vertices which contains no triangulation of the sphere, then $\mathcal{H}$ has at most $O(n^{5/2})$ edges, and this bound is the best possible up to a constant factor. Resolving a conjecture of Linial, also reiterated by Keevash, Long, Narayanan, and Scott, we show that the same result holds for triangulations of the torus. Furthermore, we extend our result to every closed orientable surface $\mathcal{S}$.

Dates et versions

hal-03236553 , version 1 (26-05-2021)

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Andrey Kupavskii, Alexandr Polyanskii, István Tomon, Dmitriy Zakharov. The extremal number of surfaces. 2021. ⟨hal-03236553⟩
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