The Brown-Erd\H{o}s-S\'os Conjecture in finite abelian groups

Jozsef Solymosi; Ching Wong

The Brown-Erd\H{o}s-S\'os Conjecture in finite abelian groups

Combinatorics 2019-01-29 v1

Authors: Jozsef Solymosi , Ching Wong

Abstract

The Brown-Erd\H{o}s-S\'{o}s conjecture, one of the central conjectures in extremal combinatorics, states that for any integer $m\geq 6,$ if a 3-uniform hypergraph on $n$ vertices contains no $m$ vertices spanning at least $m-3$ edges, then the number of edges is $o(n^2).$ We prove the conjecture for triple systems coming from finite abelian groups.

Keywords

brown-erdős-sós conjecture extremal combinatorics 3-uniform hypergraph finite abelian groups triple systems

Cite

@article{arxiv.1901.09871,
  title  = {The Brown-Erd\H{o}s-S\'os Conjecture in finite abelian groups},
  author = {Jozsef Solymosi and Ching Wong},
  journal= {arXiv preprint arXiv:1901.09871},
  year   = {2019}
}

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