Acta Informatica

, Volume 26, Issue 7, pp 657–677 | Cite as

Metatheorems for decision problems on hyperedge replacement graph languages

  • Annegret Habel
  • Hans -Jörg Kreowski
  • Walter Vogler


If a graph-theoretical property is compatible with the derivation process of hyperedge replacement graph grammars in a certain way, the property turns out to be decidable for the corresponding graph languages. More exactly speaking, we consider two 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?

In both cases, we get decidability for all hyperedge replacement graph grammars as inputs. Colorability, Hamiltonicity, and planarity are shown to be compatible so that our decidability results apply to them.


Information System Operating System Data Structure Communication Network Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Claus, V., Ehrig, H., Rozenberg, G. (eds.): Graph Grammars and Their Application to Computer Science and Biology. Lect. Notes Comput. Sci. 73 (1979)Google Scholar
  2. 2.
    Courcelle, B.: On Context-Free Sets of Graphs and Their Monadic Second-Order Theory. Lect. Notes Comput. Sci. 291, 133–146 (1987)Google Scholar
  3. 3.
    Ehrig, H., Nagl, M., Rozenberg, G. (eds.): Graph Grammars and Their Application to Computer Science, (2nd Int. Workshop). Lect. Notes Comput. Sci. 153 (1983)Google Scholar
  4. 4.
    Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds.): Graph Grammars and Their Application to Computer Science, (3rd Int. Workshop). Lect. Notes Comput. Sci. 291 (1987)Google Scholar
  5. 5.
    Habel, A.: Graph-Theoretic Properties Compatible with Graph Derivations. Proc. Graph-Theoretic Concepts in Computer Science, Lect. Notes Comput. Sci. 344, 11–29 (1989)Google Scholar
  6. 6.
    Habel, A., Kreowski, H.-J.: On Context-Free Graph Languages Generated by Edge Replacement. Lect. Notes Comput. Sci. 153, 143–158 (1983)Google Scholar
  7. 7.
    Habel, A., Kreowski, H.-J.: Characteristics of Graph Languages Generated by Edge Replacement, Theoret. Comp. Sci. 51, 81–115 (1987)Google Scholar
  8. 8.
    Habel, A., Kreowski, H.-J.: May We Introduce to You: Hyperedge Replacement. Lect. Notes Comput. Sci 291, 15–26 (1987)Google Scholar
  9. 9.
    Habel, A., Kreowski, H.-J.: Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement. Lect. Notes Comput. Sci. 247, 207–219 (1987)Google Scholar
  10. 10.
    Habel, A., Kreowski, H.-J., Vogler, W.: Compatible Graph Properties are Decidable for Hyperedge Replacement Graph Languages. EATCS Bull. 33, 55–62 (1987)Google Scholar
  11. 11.
    Habel, A., Kreowski, H.J., Vogler, W.: Decidable Boundedness Problems for Hyperedge-Replacement Graph Grammars. Proc. TAPSOFT '89. Lect. Notes Comput. Sci. 351, 275–289 (1989)Google Scholar
  12. 12.
    Janssens, D., Rozenberg, G., Welzl, E.: The Bounded Degree Problem for NLC Grammars is Decidable. J. Comput. Syst. Sci. 33, 415–422 (1986)Google Scholar
  13. 13.
    Kreowski, H.-J.: Rule Trees Can Help to Escape Hard Graph Problems. (unpublished manuscript)Google Scholar
  14. 14.
    Lautemann, C.: Decomposition Trees: Structured Graph Representation and Efficient Algorithms. Proc. CAAP '88. Lect. Notes Comput. Sci. 299, 28–39 (1988)Google Scholar
  15. 15.
    Lengauer, T.: Efficient Solution of Biconnectivity Problems on Hierarchically Defined Graphs. Proc. of the WG '85, Linz: Trauner, 201–215 (1985)Google Scholar
  16. 16.
    Lengauer, T., Wanke, E.: Efficient Analysis of Graph Properties on Context-Free Graph Languages. Proc. ICALP '88. Lect. Notes Comput. Sci. 317, 379–393 (1988)Google Scholar
  17. 17.
    Rozenberg, G., Welzl, E.: Boundary NLC Graph Grammars — Basic Definitions, Normal Forms and Complexity. Inf. Control 69, 136–167 (1986)Google Scholar
  18. 18.
    Rozenberg, G., Welzl, E.: Graph Theoretic Closure Properties of the Family of Boundary NLC Graph Languages. Acta Inf. 23, 289–309 (1986)Google Scholar
  19. 19.
    Slisenko, A.O.: Context-Free Grammars as a Tool for Describing Polynomial-Time Subclasses of Hard Problems. Inf. Proc. Lett. 14, 52–56 (1982)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Annegret Habel
    • 1
  • Hans -Jörg Kreowski
    • 1
  • Walter Vogler
    • 2
  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremen 33Federal Republic of Germany
  2. 2.Institut für InformatikTechnische Universität MünchenMünchen 2Federal Republik of Germany

Personalised recommendations