On the divisibility of homogeneous hypergraphs
type: Item
instance of: scholarly article
title: On the divisibility of homogeneous hypergraphs
zbMATH Open document ID: 0803.05043
DOI: 10.1007/BF01215348
author: Norbert Sauer
author: Mohamed H. El-Zahar
published in: Combinatorica
publication date: 1994-08-11T00:00:00Z
review text: Let \(k\geq 3\) and \(T\) be a family of \(k\)-hypergraphs in which every 3- element subset of the ground set is covered by a member of \(T\). Then the countable homogeneous \(T\)-free hypergraph is indivisible, i.e., has the vertex Ramsey property. A weaker property is described if the covering of pairs is satisfied. Other properties as well as a counterexample are also given.
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 617053
zbMATH Keywords: divisibility
zbMATH Keywords: homogeneous hypergraphs
zbMATH Keywords: hypergraph
zbMATH Keywords: Ramsey property
reviewed by: Péter Komjáth
MaRDI profile type: Publication
cites work: Q3671169
cites work: Ramsey-type properties of relational structures
cites work: The indivisibility of the homogeneous \(K_ n\)-free graphs
cites work: Countable Ultrahomogeneous Undirected Graphs
cites work: Coloring of universal graphs
full work available at URL: https://doi.org/10.1007/bf01215348
OpenAlex ID: W2068338148
description: scientific article; zbMATH DE number 617053