Publications - Published papers

Please find below publications of our group. Currently, we list 496 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 (access) is restricted to our local network and chosen collaborators. If you have problems accessing electronic information, please let us know:

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The Cartesian Product of Hypergraphs

Lydia Ostermeier, Marc Hellmuth, Peter F. Stadler

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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