University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Turán densities for hypergraph with quasirandom links

Turán densities for hypergraph with quasirandom links

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If you have a question about this talk, please contact Eoin Long.

Reiher, Rödl, and Schacht proved that 3-uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than $(r-2)/(r-3)$ contain a clique on $2^r$ vertices. This result turned out to be asymptotically best possible for several cliques up to size 16. Their proof is based on an application of the regularity method for hypergraphs. Here we find a substantially simpler proof of this result based mainly on supersaturation arguments. In fact this new approach allows us to obtain slightly more general results.

Additionally, for the appropriately defined Turán density for this context, we establish a general bound for the Turán density of $K_{2r}$ with respect to the Turán density of $K_r$. This is a joint work with Berger, Reiher, Rödl, and Schacht.

This talk is part of the Combinatorics and Probability seminar series.

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