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International Conference on Relational and Algebraic Methods in Computer Science

RAMICS 2012: Relational and Algebraic Methods in Computer Science pp 326–341Cite as

Relations on Hypergraphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7560))

Abstract

A relation on a hypergraph is a binary relation on the set consisting of the nodes and hyperedges together, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join-preserving mappings on the lattice of sub-hypergraphs. This paper studies the algebra of these relations, in particular the analogues of the familiar operations of complement and converse of relations. When generalizing from relations on a set to relations on a hypergraph we find that the Boolean algebra of relations is replaced by a weaker structure: a pair of isomorphic bi-Heyting algebras, one of which arises from the relations on the dual hypergraph. The paper also considers the representation of sub-hypergraphs as relations and applies the results obtained to mathematical morphology for hypergraphs.

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Author information

Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, U.K.

    John G. Stell

Authors
  1. John G. Stell
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Editor information

Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  2. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, CB3 0FD, Cambridge, UK

    Timothy G. Griffin

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© 2012 Springer-Verlag Berlin Heidelberg

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Stell, J.G. (2012). Relations on Hypergraphs. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-33314-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33313-2

  • Online ISBN: 978-3-642-33314-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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