The Cartesian Product of Hypergraphs

Authors:
Lydia Ostermeier;Marc Hellmuth;Peter F. Stadler
Affiliations:
Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, Leipzig, D-04103, Germany and Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinforma ...;Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, Leipzig, D-04103, Germany and Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinforma ...;Rnomics Group, Fraunhofer Institut Für Zelltherapie und Immunologie, Leipzig, Deutscher Platz 5E D-04103Germany and Department of Theoretical Chemistry University of Vienna, Währinge ...
Venue:
Journal of Graph Theory
Year:
2012

Citing 5
Cited 1

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Factorization of products of hypergraphs: Structure and algorithms

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Abstract

We show that every simple, (weakly) connected, possibly directed and infinite, hypergraph has a unique prime factor decomposition with respect to the (weak) Cartesian product, even if it has infinitely many factors. This generalizes previous results for graphs and undirected hypergraphs to directed and infinite hypergraphs. The proof adopts the strategy outlined by Imrich and Žerovnik for the case of graphs and introduces the notion of diagonal-free grids as a replacement of the chord-free 4-cycles that play a crucial role in the case of graphs. This leads to a generalization of relation Δ on the arc set, whose convex hull is shown to coincide with the product relation of the prime factorization. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.