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 (
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) is restricted to our local network and chosen collaborators.
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Strong products of hypergraphs: Unique prime factorization theorems and algorithms
Hellmuth M, Ostermeier L, Noll M
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Status: Published
Discrete Applied Mathematics 171 (2014): 60-71
Abstract
It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation.
In this contribution, we show that every connected thin hypergraph H
has a unique prime factorization with respect to the normal and strong (hypergraph) product. Both products coincide with the usual strong graph product whenever H
is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as a natural generalization of the Cartesian skeleton of graphs and prove that it is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian skeleton of hypergraphs can be determined in O(|E|2)
time and that the PFD can be computed in O(|V|2|E|)
time, for hypergraphs H=(V,E)
with bounded degree and bounded rank.
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