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Original Article
The Cartesian product of hypergraphs
Article first published online: 26 APR 2011
DOI: 10.1002/jgt.20609
© 2012 Wiley Periodicals, Inc.
Additional Information
How to Cite
Ostermeier, L., Hellmuth, M. and Stadler, P. F. (2012), The Cartesian product of hypergraphs. J. Graph Theory, 70: 180–196. doi: 10.1002/jgt.20609
Publication History
- Issue published online: 25 APR 2012
- Article first published online: 26 APR 2011
- Manuscript Revised: 10 FEB 2011
- Manuscript Received: 11 MAY 2010
- Abstract
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- Cited By
Keywords:
- directed hypergraph;
- hypergraph;
- weak Cartesian product;
- prime factor decomposition;
- grid-property
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