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A Survey on Hypergraph Products |
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| Authors: | Marc Hellmuth Lydia Ostermeier Peter F Stadler |
| Institution: | 1. Center for Bioinformatics, Saarland University, Building E 2.1, Room 413, P.O. Box 15 11 50, 66041, Saarbr??cken, Germany 2. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany 3. Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinformatics, University of Leipzig, H?rtelstrasse 16-18, 04107, Leipzig, Germany 4. RNomics Group, Fraunhofer Institut f??r Zelltherapie und Immunologie, Deutscher Platz 5e, 04103, Leipzig, Germany 5. Department of Theoretical Chemistry, University of Vienna, W?hringerstra?e 17, 1090, Vienna, Austria 6. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA |
| 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. |
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