Turán density of cliques of order five in 3-uniform hypergraphs with quasirandom links

Sören Berger; Simon Piga; Christian Reiher; Vojtěch Rödl; Mathias Schacht

doi:10.1016/j.procs.2021.11.050

Turán density of cliques of order five in 3-uniform hypergraphs with quasirandom links

Sören Berger, Simon Piga, Christian Reiher, Vojtěch Rödl, Mathias Schacht

Mathematics

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Abstract

We show that 3-uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than 1/3 contain a clique on five vertices. This result is asymptotically best possible.

Original language	English
Pages (from-to)	412-418
Journal	Procedia Computer Science
Volume	195
DOIs	https://doi.org/10.1016/j.procs.2021.11.050
Publication status	Published - 5 Jan 2022

Keywords

Hypergraphs
Turán’s problem
extremal graph theory
quasirandomness

Access to Document

10.1016/j.procs.2021.11.050Licence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

BergerS2021TuránFinal published version, 377 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Cite this

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title = "Tur{\'a}n density of cliques of order five in 3-uniform hypergraphs with quasirandom links",

abstract = "We show that 3-uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than 1/3 contain a clique on five vertices. This result is asymptotically best possible.",

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AU - Piga, Simon

AU - Reiher, Christian

AU - Rödl, Vojtěch

AU - Schacht, Mathias

PY - 2022/1/5

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AB - We show that 3-uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than 1/3 contain a clique on five vertices. This result is asymptotically best possible.

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KW - Turán’s problem

KW - extremal graph theory

KW - quasirandomness

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