On Turán numbers for disconnected hypergraphs

R. Mulas, J. Nie*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

20 Downloads (Pure)

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 languageEnglish
Pages (from-to)168-182
Number of pages15
JournalActa Mathematica Hungarica
Volume170
Issue number1
Early online date25 May 2023
DOIs
Publication statusPublished - Jun 2023

Bibliographical note

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

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

Fingerprint

Dive into the research topics of 'On Turán numbers for disconnected hypergraphs'. Together they form a unique fingerprint.

Cite this