Publications - Published papers

Please find below publications of our group. Currently, we list 500 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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A Survey on Hypergraph Products

Marc Hellmuth, Lydia Ostermeier, and Peter F. Stadler

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Math. Comp. Sci. 6: 1-32 (2012)

Abstract


A surprising diversity of different products of hypergraphs have been discussed in the literature. Most of the hypergraph products can be viewed as generalizations of one of the four standard graph products. The most widely studied variant, the so-called square product, does not have this property, however. Here we survey the literature on hypergraph products with an emphasis on comparing the alternative generalizations of graph products and the relationships among them. In this context the so-called 2-sections and L2-sections are considered. These constructions are closely linked to related colored graph structures that seem to be a useful tool for the prime factor decompositions w.r.t. specific hypergraph products. We summarize the current knowledge on the propagation of hypergraph invariants under the different hypergraph multiplications. While the overwhelming majority of the material concerns finite (undirected) hypergraphs, the survey also covers a summary of the few results on products of infinite and directed hypergraphs.

Keywords


Hypergraph invariants, products, set systems