The Modular Decomposition of Countable Graphs: Constructions in Monadic Second-Order Logic

  • Bruno Courcelle
  • Christian Delhommé
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3634)


We show that the modular decomposition of a countable graph can be defined from this graph, given with an enumeration of its set of vertices, by formulas of Monadic Second-Order logic. A second main result is the definition of a representation of modular decompositions by a low degree relational structures, also constructible by Monadic Second-Order formulas.


Binary Tree Strong Module Hasse Diagram Graph Operation Automatic Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bruno Courcelle
    • 1
  • Christian Delhommé
    • 2
  1. 1.LaBRI CNRSUniversité Bordeaux 1 
  2. 2.ERMITUniversité de La Réunion 

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