Dániel Gerbner: General lemmas for Berge-Turán hypergraph problems

For a graph F, a hypergraph H is a Berge copy of F (or a Berge-F in short), if there

is a bijection f:E(F)→E(H) such that for each $e\in E(F)$ we have $e\subset f(e)$. A hypergraph

is Berge-F-free if it does not contain a Berge copy of F. We denote the maximum

number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by $ex_(n,Berge-F)$.

We prove two general lemmas concerning the maximum size of a Berge-F-free

hypergraph and use them to establish new results and improve several old results.

link: https://arxiv.org/abs/1808.10842

Joint work with Abhishek Methuku and Cory Palmer