Graph-theoretic properties compatible with graph derivations

  • Annegret Habel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 344)


A graph-theoretic property is compatible with the rewriting process of hyperedge-replacement graph grammars if for each graph and each derivation of it the property holds just in case the property (or a related property) holds for some specific subgraphs determined by the fibres of the derivation. On the one hand, this leads to proper tests of compatible properties. On the other hand, compatible properties turn out to be decidable for the corresponding graph languages, i.e., the questions
  1. (1)

    Is there a graph in the generated language having the property?

  2. (2)

    Do all graphs in the generated language have the property? are decidable for all hyperedge-replacement graph grammars as inputs. In this paper, we introduce the concept of compatible properties, show the compatibility of connectedness, existence of Eulerian paths and cycles, and edge-colorability, and apply the decidability result to these distinguished properties.



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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Annegret Habel
    • 1
  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremen 33

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