Ramsey properties of random hypergraphs
type: Item
instance of: scholarly article
title: Ramsey properties of random hypergraphs
zbMATH Open document ID: 0893.05011
author: Vojtěch Rödl
author: Andrzej Ruciński
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-08-02T00:00:00Z
review text: Let \(K^{(k)} (n,p)\) denote the random \(k\)-uniform hypergraph obtained by the independent inclusion of each of the \({n\choose k}\) \(k\)-subsets with probability \(p\). If \(F\) and \(G\) are two \(k\)-uniform hypergraphs, the Ramsey theory arrow notation, \(F\to(G)^e_r\), stands for the statement: For every partition of the edges of \(F\) into \(r\) classes, at least one of the classes contains a copy of \(G\). The main result of this paper is Theorem 1.4: There exists an absolute constant \(C>0\) such that \(\lim_{n\to\infty} P(K^{(3)} (n,p)\to (K_4^{(3)})_2^{e}) =1\) for \(p>Cn^{-{1 \over 3}}\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 1123546
zbMATH Keywords: random \(k\)-uniform hypergraph
zbMATH Keywords: Ramsey theory
reviewed by: Jack E. Graver
MaRDI profile type: Publication
OpenAlex ID: W1974683938
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DOI: 10.1006/JCTA.1997.2785
description: scientific article; zbMATH DE number 1123546