Abstract
Reiher, Rödl and Schacht [J. London Math. Soc. 97 (2018), 77–97] 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.
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.
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Garbe, F., Král’, D., Lamaison, A. (2021). Hypergraphs with Minimum Positive Uniform Turán Density. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_24
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