Hypergraphs with minimum positive uniform Tur\'an density

Frederik Garbe; Daniel Kral; Ander Lamaison

Hypergraphs with minimum positive uniform Tur\'an density

Combinatorics 2022-01-17 v2

Authors: Frederik Garbe , Daniel Kral , Ander Lamaison

Abstract

Reiher, R\"odl and Schacht [J. London Math. Soc. 97 (2018), 77--97] showed that the uniform Tur\'an density of every $3$ -uniform hypergraph is either $0$ or at least $1/27$ , and asked whether there exist $3$ -uniform hypergraphs with uniform Tur\'an density equal or arbitrarily close to $1/27$ . We construct $3$ -uniform hypergraphs with uniform Tur\'an density equal to $1/27$ .

Keywords

turán theory hypergraph theory

Cite

@article{arxiv.2105.09883,
  title  = {Hypergraphs with minimum positive uniform Tur\'an density},
  author = {Frederik Garbe and Daniel Kral and Ander Lamaison},
  journal= {arXiv preprint arXiv:2105.09883},
  year   = {2022}
}

Comments

22 pages, 9 figures; updated version with several small corrections and an added section with conclusive remarks

Hypergraphs with minimum positive uniform Tur\'an density

Abstract

Keywords

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