Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
) is restricted to our local network and chosen collaborators.
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) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
The Cartesian Product of Hypergraphs
Lydia Ostermeier, Marc Hellmuth, Peter F. Stadler
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Status: Published
J. Graph Theory 70: 180-196 (2012)
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 Zerovnik for the
case of graphs and introduced 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 {delta} on
the arc set, whose convex hull is shown to coincide with the product
relation of the prime factorization.
Keywords
directed Hypergraph, Hypergraph, weak Cartesian Product, Prime Factor Decomposition, grid property