Hypergraphs with minimum positive uniform Tur\'an density
Frederik Garbe, Daniel Kral, Ander Lamaison

TL;DR
This paper constructs 3-uniform hypergraphs with a uniform Turán density exactly equal to 1/27, addressing a question about the possible values of this density.
Contribution
The authors provide the first explicit construction of 3-uniform hypergraphs with Turán density exactly 1/27, demonstrating that this value is attainable.
Findings
Constructed hypergraphs with Turán density exactly 1/27
Confirmed the density value is achievable, answering a prior open question
Contributed to understanding the range of Turán densities for 3-uniform hypergraphs
Abstract
Reiher, R\"odl and Schacht [J. London Math. Soc. 97 (2018), 77--97] showed that the uniform Tur\'an density of every -uniform hypergraph is either or at least , and asked whether there exist -uniform hypergraphs with uniform Tur\'an density equal or arbitrarily close to . We construct -uniform hypergraphs with uniform Tur\'an density equal to .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory
