On hypergraphs with every four points spanning at most two triples
type: Item
instance of: scholarly article
title: On hypergraphs with every four points spanning at most two triples
zbMATH Open document ID: 1023.05105
author: Dhruv Mubayi
published in: The Electronic Journal of Combinatorics
publication date: 2003-09-24T00:00:00Z
full work available at URL: https://eudml.org/doc/122970
full work available at URL: v10i1n10.html
review text: Summary: Let \(\mathcal F\) be a triple system on an \(n\)-element set. Suppose that \(\mathcal F\) contains more than \((1/3-\varepsilon)\left ( \begin{smallmatrix} n \\ 3 \end{smallmatrix}\right) \) triples, where \(\varepsilon > 10^{-6}\) is explicitly defined and \(n\) is sufficiently large. Then there is a set of four points containing at least three triples of \(\mathcal F\). This improves previous bounds of \textit{D. de Caen} [Ars Comb. 16, 5-10 (1983; Zbl 0532.05037)] and \textit{U. Matthias} [Hypergraphs without complete \(r\)-partite subgraphs (German) (Heidelberg: Univ., Naturwiss.-Mathemat. Gesamtfak.) (1994; Zbl 0818.05048)].
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 1985385
MaRDI profile type: Publication
Recommended article: On the density of 2-colorable 3-graphs in which any four points span at most two edges
Recommended article: On 3‐graphs with no four vertices spanning exactly two edges
Recommended article: Triangulating graphs with few \(P_4\)'s
Recommended article: Four-connected triangulations of planar point sets
Recommended article: On Four-Connecting a Triconnected Graph
Recommended article: On 3-Hypergraphs with Forbidden 4-Vertex Configurations
Recommended article: Q4230328
Recommended article: 4-Connected triangulations on few lines
Recommended article: 4-connected triangulations on few lines
Recommended article: Q4004435
description: scientific article; zbMATH DE number 1985385