Cayley, Marty and Schreier hypergraphs
type: Item
instance of: scholarly article
title: Cayley, Marty and Schreier hypergraphs
zbMATH Open document ID: 0820.05049
DOI: 10.1007/BF02940782
author: Marco Buratti
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1995-08-27T00:00:00Z
review text: In this paper, Cayley, Marty and Schreier hypergraphs are defined. Many properties of these hypergraphs are proved. Typical results are: (i) Every projective plane \(\text{PG} (2,q)\) with \(q^ 2 + q + 1\) a prime, is a connected and sharply vertex-transitive hypergraph of rank \(q + 1\) but is not a \((q + 1)\)-Cayley hypergraph (G. Sabidussi proved in 1958 that any connected and sharply vertex-transitive graph is a Cayley graph); (ii) Every simple hypergraph \(H\) is a generalized Schreier hypergraph. In the last two sections, a characterization of linear spaces in terms of generalized Schreier hypergraphs and a relation between a connected graph admitting a regular \(k\)-edge-colouring and a Cayley graph are proved.
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 706670
zbMATH Keywords: Cayley hypergraphs
zbMATH Keywords: Marty hypergraphs
zbMATH Keywords: Schreier hypergraphs
zbMATH Keywords: projective plane
zbMATH Keywords: sharply vertex-transitive hypergraph
zbMATH Keywords: Cayley graphs
zbMATH Keywords: hypergraph
zbMATH Keywords: characterization of linear spaces
reviewed by: H. P. Yap
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 706670