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Hypergraphs with minimum positive uniform Turán density

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Abstract

Reiher, Rödl and Schacht showed that the uniform Turán density of every 3-uniform hypergraph is either 0 or at least 1/27, and asked whether there exist 3-uniform hypergraphs with uniform Turán density equal or arbitrarily close to 1/27. We construct 3-uniform hypergraphs with uniform Turán density equal to 1/27.

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Acknowledgements

The authors would like to thank Jacob Cooper for his comments on the topics covered in this paper. We would also like to thank the anonymous referee for their careful review of the manuscript and for their many helpful comments.

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68A, 602 00, Brno, Czech Republic

    Frederik Garbe, Daniel Král’ & Ander Lamaison

Authors
  1. Frederik Garbe
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  2. Daniel Král’
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  3. Ander Lamaison
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Corresponding author

Correspondence to Frederik Garbe.

Additional information

This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 648509). This publication reflects only its authors’ view; the European Research Council Executive Agency is not responsible for any use that may be made of the information it contains. The authors were also supported by the MUNI Award in Science and Humanities of the Grant Agency of Masaryk University.

An extended abstract containing the results presented in this paper has appeared in the proceedings of EuroComb’21.

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Garbe, F., Král’, D. & Lamaison, A. Hypergraphs with minimum positive uniform Turán density. Isr. J. Math. 259, 701–726 (2024). https://doi.org/10.1007/s11856-023-2554-0

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  • DOI: https://doi.org/10.1007/s11856-023-2554-0

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