Geodesic
On a Turán problem in weakly quasirandom 3-uniform hypergraphs
Journal of the European Mathematical Society, Tome 20 (2018) no. 5, pp. 1139-1159.

Voir la notice de l'article provenant de la source EMS Press

Extremal problems for 3-uniform hypergraphs are known to be very difficult and despite considerable effort the progress has been slow. We suggest a more systematic study of extremal problems in the context of quasirandom hypergraphs. We say that a 3-uniform hypergraph H=(V,E) is weakly (d,η)-quasirandom if for any subset U⊆V the number of hyperedges of H contained in U is in the interval d(3∣U∣​)±η∣V∣3. We show that for any ε>0 there exists η>0 such that every sufficiently large weakly (1/4+ε,η)-quasirandom hypergraph contains four vertices spanning at least three hyperedges. This was conjectured by Erdős and Sós and it is known that the density 1/4 is best possible.
DOI : 10.4171/jems/784
Classification : 05-XX
Mots-clés : Quasirandom hypergraphs, extremal graph theory, Turán's problem 
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     title = {On a {Tur\'an} problem in weakly quasirandom 3-uniform hypergraphs},
     journal = {Journal of the European Mathematical Society},
     pages = {1139--1159},
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Christian Reiher; Vojtěch Rödl; Mathias Schacht. On a Turán problem in weakly quasirandom 3-uniform hypergraphs. Journal of the European Mathematical Society, Tome 20 (2018) no. 5, pp. 1139-1159. doi : 10.4171/jems/784. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/784/

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