Combinatorial hypermap rewriting

  • Eric Sopena
Theoretical Aspects 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 256)


Combinatorial hypermaps may be viewed as topological representations of hypergraphs. In this paper, we introduce a hypermap rewriting model, based on a purely combinatorial formulation of the rewriting mechanism. We illustrate this definition by providing a hypermap grammar which generates the set of all connected planar maps. We also investigate a special kind of hypermap grammars, the H-grammars, for which we give a Pumping Theorem enlightening the combinatorial structure of the generated hypermap languages.


  1. [1]
    M. BAUDERON, B. COURCELLE, "Graph Expressions and Graph Rewritings", Rapport interne no I-8623, Université de Bordeaux I, Sept. 1986.Google Scholar
  2. [2]
    V. CLAUS, H. EHRIG, G. ROZENBERG, "Graph Grammars and their Application to Computer Science and Biology", LNCS 73, Springer-Verlag, 1980.Google Scholar
  3. [3]
    R. CORI, "Un code pour les graphes planaires et ses applications", Astérique 27, 1975.Google Scholar
  4. [4]
    J. EDMONDS, "A Combinatorial Representation for Polyhedral Surfaces", Not. Amer. Math. Soc. 7, 1960.Google Scholar
  5. [5]
    H. EHRIG, "Introduction to the Algebraic Theory of Graph Grammars", LNCS 56, 1977, pp. 245–255.Google Scholar
  6. [6]
    H. EHRIG, M. NAGL, G. ROZENBERG, "Graph Grammars and their Application to Computer Science", LNCS 153, Springer-Verlag, 1983.Google Scholar
  7. [7]
    A. HABEL, H.J. KREOWSKI, "Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement", Preprint, Oct. 1985.Google Scholar
  8. [8]
    D. JANSSENS, "Node-Label-Controlled Graph Grammars", Ph.D. Thesis, Univ. of Antwerpen, 1983.Google Scholar
  9. [9]
    E. SOPENA, "Réécriture d'hypercartes combinatoires et conception d'un langage pour la programmation d'algorithmes de graphes", Thèse de Doctorat, Université de Bordeaux I, Nov. 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Eric Sopena
    • 1
  1. 1.Département InformatiqueI.U.T. "A", Université de Bordeaux ITalence

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