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Hypergraph Based Berge Hypergraphs

Publikace na Matematicko-fyzikální fakulta |
2022

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

Fix a hypergraph F. A hypergraph H is called a Berge copy of F or Berge-F if we can choose a subset of each hyperedge of H to obtain a copy of F.

A hypergraph H is Berge-F-free if it does not contain a subhypergraph which is Berge copy of F. This is a generalization of the usual, graph-based Berge hypergraphs, where F is a graph.

In this paper, we study extremal properties of hypergraph based Berge hypergraphs and generalize several results from the graph-based setting. In particular, we show that for any r-uniform hypergraph F, the sum of the sizes of the hyperedges of a (not necessarily uniform) Berge-F-free hypergraph H on n vertices is o(n(r)) when all the hyperedges of H are large enough.

We also give a connection between hypergraph based Berge hypergraphs and generalized hypergraph Turan problems.