Geodesic
An irrational Turán density via hypergraph Lagrangian densities
Biao Wu1
1Hunan Normal University
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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Baber and Talbot asked whether there is an irrational Turán density of a single hypergraph. In this paper, we show that the Lagrangian density of a 4-uniform matching of size 3 is an irrational number. Sidorenko showed that the Lagrangian density of an r-uniform hypergraph F is the same as the Turán density of the extension of F. Therefore, our result gives a positive answer to the question of Baber and Talbot. We also determine the Lagrangian densities of a class of r-uniform hypergraphs on n vertices with θ(n2) edges. As far as we know, for every hypergraph F with known hypergraph Lagrangian density, the number of edges in F is less than the number of its vertices.
DOI : 10.37236/10645
Classification : 05D05, 05C65, 05C30
Mots-clés : maximal number of edges, Turán problem

Biao Wu  1

1 Hunan Normal University 
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     author = {Biao Wu},
     title = {An irrational {Tur\'an} density via hypergraph {Lagrangian} densities},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
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     doi = {10.37236/10645},
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Biao Wu. An irrational Turán density via hypergraph Lagrangian densities. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10645

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