@inbook{5f7aebc4619c43bfa40a9dca810b063e,

title = "Unavoidable Hypergraphs",

abstract = "The following very natural problem was raised by Chung and Erd{\H o}s in the early 80{\textquoteright}s. What is the minimum of the Tur{\'a}n number ex (n, H) among all r-graphs H with a fixed number of edges? Their actual focus was on an equivalent and perhaps even more natural question which asks what is the largest size of an r-graph that can not be avoided in any r-graph on n vertices and e edges? In the original paper they resolve this question asymptotically for graphs, for most of the range of e. In a follow-up work Chung and Erd{\H o}s resolve the 3-uniform case and raise the 4-uniform case as the natural next step. In this paper we make first progress on this problem in over 40 years by asymptotically resolving the 4-uniform case which gives us some indication on how the answer should behave in general.",

keywords = "Hypergraphs, Tur{\'a}n numbers, Unavoidable graphs",

author = "Matija Buci{\'c} and Nemanja Dragani{\'c} and Benny Sudakov and Tuan Tran",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-83823-2_53",

language = "English (US)",

series = "Trends in Mathematics",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "339--344",

booktitle = "Trends in Mathematics",

address = "Germany",

}