On the maximal number of edges in a homogeneous hypergraph not containing prohibited subgraphs
type: Item
instance of: scholarly article
title: On the maximal number of edges in a homogeneous hypergraph not containing prohibited subgraphs
zbMATH Open document ID: 0677.05064
DOI: 10.1007/BF01158259
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: The author proves that the maximal number of edges of a 4-uniform hypergraph with n vertices without two edges whose symmetric difference is contained in a third is equal to \(\lfloor n/4\rfloor \lfloor (n+1)/4\rfloor \lfloor (n+2)/4\rfloor \lfloor (n+3)/4\rfloor\) and that the extremal hypergraph is unique up to isomorphism. This settles a conjecture of \textit{B. Bollobás}, who solved the corresponding problem for 3-uniform hypergraphs [Discrete Math. 8, 21-24 (1974; Zbl 0291.05114)].
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 4108826
zbMATH Keywords: maximal number of edges
zbMATH Keywords: extremal hypergraph
author: Alexander Sidorenko
MaRDI profile type: Publication
cites work: On the combinatorial problems which I would most like to see solved
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cites work: Q3312262
cites work: Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures
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description: scientific article; zbMATH DE number 4108826