@article{8db16ecc39e5435fade29719219accf3,
title = "Hypergraph Based Berge Hypergraphs",
abstract = "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(nr) when all the hyperedges of H are large enough. We also give a connection between hypergraph based Berge hypergraphs and generalized hypergraph Tur{\'a}n problems.",
keywords = "Berge hypergraphs, Sypergraph Tur{\'a}n problems",
author = "Martin Balko and D{\'a}niel Gerbner and Kang, {Dong Yeap} and Younjin Kim and Cory Palmer",
note = "Funding Information: M. Balko was supported by the Grant No. 19-04113Y of the Czech Science Foundation (GA{\v C}R) and by the Center for Foundations of Modern Computer Science (Charles University project UNCE/SCI/004). D. Gerbner was supported in part by the J{\'a}nos Bolyai Research Fellowship of the Hungarian Academy of Sciences and the National Research, Development and Innovation Office - NKFIH under the Grants K 116769, KH 130371 and SNN 12936. D. Kang was supported by the Institute for Basic Science, No. IBS-R029-C1, and the research leading to these results was also supported by the EPSRC, grant nos. EP/N019504/1. Y. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A04005963). C. Palmer was supported by a grant from the Simons Foundation #712036. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.",
year = "2022",
month = feb,
day = "1",
doi = "10.1007/s00373-021-02419-1",
language = "English",
volume = "38",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Japan",
number = "1",
}