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Mathematics in Computer Science

, Volume 6, Issue 1, pp 1–32 | Cite as

A Survey on Hypergraph Products

  • Marc Hellmuth
  • Lydia Ostermeier
  • Peter F. StadlerEmail author
Article

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 

Mathematics Subject Classification (2000)

Primary 99Z99 Secondary 00A00 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Marc Hellmuth
    • 1
  • Lydia Ostermeier
    • 2
    • 3
  • Peter F. Stadler
    • 2
    • 3
    • 4
    • 5
    • 6
    Email author
  1. 1.Center for BioinformaticsSaarland UniversitySaarbrückenGermany
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for BioinformaticsUniversity of LeipzigLeipzigGermany
  4. 4.RNomics GroupFraunhofer Institut für Zelltherapie und ImmunologieLeipzigGermany
  5. 5.Department of Theoretical ChemistryUniversity of ViennaViennaAustria
  6. 6.Santa Fe InstituteSanta FeUSA

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