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Paths and cycles of hypergraphs

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Abstract

Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Jianfang Wang

  2. Department of Information Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

    Tony T. Lee

Authors
  1. Jianfang Wang
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  2. Tony T. Lee
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Wang, J., Lee, T.T. Paths and cycles of hypergraphs. Sci. China Ser. A-Math. 42, 1–12 (1999). https://doi.org/10.1007/BF02872044

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  • DOI: https://doi.org/10.1007/BF02872044

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