Stability theorems for cancellative hypergraphs
type: Item
instance of: scholarly article
title: Stability theorems for cancellative hypergraphs
zbMATH Open document ID: 1052.05051
author: Dhruv Mubayi
author: Peter Keevash
published in: Journal of Combinatorial Theory. Series B
publication date: 2004-10-01T00:00:00Z
review text: A cancellative hypergraph has no three edges \(A,B,C\) with \(A\bigtriangleup B \subset C.\) The paper gives a short proof for Bollobás's result: the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. It also shows that the system \(F_5=\{abc,abd,cde\}\) (one of the two forbidden configurations in a cancellative hypergraph) itself enforces that maximum cardinality of a triple system, not containing a copy of \(F_5\), also achieved by the same extremal triple system (in case of \(n>32\), highly strengthening an earlier result of Frankl and Füredi). Finally it also proves stability results for both problems.
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 2104555
zbMATH Keywords: cancellative hypergraph
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
full work available at URL: j.jctb.2004.05.003
OpenAlex ID: W2110639574
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DOI: 10.1016/J.JCTB.2004.05.003
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description: scientific article; zbMATH DE number 2104555