On Turán numbers for disconnected hypergraphs

R. Mulas; J. Nie

doi:10.1007/s10474-023-01340-8

On Turán numbers for disconnected hypergraphs

R. Mulas
, J. Nie^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

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Abstract

We introduce the following simpler variant of the Turán problem: Given integers n> k> r≥ 2 and m≥ 1 , what is the smallest integer t for which there exists an r -uniform hypergraph with n vertices, t edges and m connected components such that any k -subset of the vertex set contains at least one edge? We prove some general estimates for this quantity and for its limit, normalized by (nr) , as n→ ∞ . Moreover, we give a complete solution of the problem for the particular case when k= 5 , r= 3 and m≥ 2 .

Original language	English
Pages (from-to)	168-182
Number of pages	15
Journal	Acta Mathematica Hungarica
Volume	170
Issue number	1
Early online date	25 May 2023
DOIs	https://doi.org/10.1007/s10474-023-01340-8
Publication status	Published - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023, Akadémiai Kiadó, Budapest, Hungary.

Funding

Raffaella Mulas was supported by the Max Planck Society’s Minerva Grant.

Keywords

hypergraph
Turán number
Turán problem

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10.1007/s10474-023-01340-8

On Turán numbers for disconnected hypergraphsFinal published version, 341 KBLicence: Article 25fa Dutch Copyright Act

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On Turán numbers for disconnected hypergraphs

Abstract

Bibliographical note

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Keywords

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