Constructing dense GRID-Free linear 3-graphs

Lior Gishboliner; Asaf Shapira

doi:10.1090/proc/15673

Constructing dense GRID-Free linear 3-graphs

Lior Gishboliner, Asaf Shapira

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Review article › peer-review

Abstract

We show that there exist linear 3-uniform hypergraphs with n vertices and Ω(n²) edges which contain no copy of the 3 × 3 grid. This makes significant progress on a conjecture of Füredi and Ruszinkó. We also discuss connections to proving lower bounds for the (9, 6) Brown-Erdos-Sós problem and to a problem of Solymosi and Solymosi.

Original language	English
Pages (from-to)	69-74
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	1
DOIs	https://doi.org/10.1090/proc/15673
State	Published - 2022

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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10.1090/proc/15673

Cite this

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title = "Constructing dense GRID-Free linear 3-graphs",

abstract = "We show that there exist linear 3-uniform hypergraphs with n vertices and Ω(n2) edges which contain no copy of the 3 × 3 grid. This makes significant progress on a conjecture of F{\"u}redi and Ruszink{\'o}. We also discuss connections to proving lower bounds for the (9, 6) Brown-Erdos-S{\'o}s problem and to a problem of Solymosi and Solymosi.",

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note = "Publisher Copyright: 2021 American Mathematical Society",

year = "2022",

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DO - 10.1090/proc/15673

M3 - مقالة مرجعية

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Constructing dense GRID-Free linear 3-graphs

Abstract

All Science Journal Classification (ASJC) codes

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