Directed Moore hypergraphs
type: Item
instance of: scholarly article
title: Directed Moore hypergraphs
zbMATH Open document ID: 0839.05076
DOI: 10.1016/0166-218X(94)00069-P
author: Fahir Ö. Ergincan
author: D. A. Gregory
published in: Discrete Applied Mathematics
publication date: 1996-06-05T00:00:00Z
review text: For any directed hypergraph \(H\) with \(n\) vertices, maximum out-degree \(d^+\), maximum out-size \(s^+\) and diameter \(D\) we have \(n\leq \sum^D_{i= 0} (d^+ s^+)^i\). The authors prove a conjecture of Jean-Claude Bermond, which states that this bound cannot be attained if \(D> 1\) unless \(H\) is a directed cycle. Directed hypergraphs that attain this bound are called directed Moore hypergraphs. In addition, the authors prove that directed Moore hypergraphs can be identified with certain kinds of matrix factorizations.
reviewed by: Klaus Dohmen
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 822835
zbMATH Keywords: directed hypergraph
zbMATH Keywords: conjecture of Jean-Claude Bermond
zbMATH Keywords: directed Moore hypergraphs
zbMATH Keywords: matrix factorizations
MaRDI profile type: Publication
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Wikidata QID: Q127957294
full work available at URL: 0166-218x(94)00069-p
OpenAlex ID: W1977902503
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description: scientific article; zbMATH DE number 822835