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Enumeration of Maximum Acyclic Hypergraphs

Enumeration of Maximum Acyclic Hypergraphs Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be $$ {\left( {\begin{array}{*{20}c} {n} \\ {{r - 1}} \\ \end{array} } \right)}{\left( {n{\left( {r - 1} \right)} - r^{2} + 2r} \right)}^{{n - r - 1}} . $$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Enumeration of Maximum Acyclic Hypergraphs

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s102550200020
Publisher site
See Article on Publisher Site

Abstract

Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be $$ {\left( {\begin{array}{*{20}c} {n} \\ {{r - 1}} \\ \end{array} } \right)}{\left( {n{\left( {r - 1} \right)} - r^{2} + 2r} \right)}^{{n - r - 1}} . $$

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2002

References