The definition in monadic second-order logic of modular decompositions of ordered graphs

  • Bruno Courcelle
Structure and Logic of Graphs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1073)


Every graph can be represented uniquely in a hierarchical way by means of its modular decomposition. We establish that the modular decomposition of a linearly ordered graph is definable in monadic second-order (MS) logic in the graph itself. The modular decomposition does not depend on the linear order of the given graph. A set of graphs is recognizable w.r.t. the operations associated with graph substitution iff it is definable by a formula of an extension of MS logic based on the use of auxilliary linear orderings. This paper is an extended abstract: complete proofs can be found in [7].


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.Laboratoire associé au CNRSUniversité Bordeaux-ITalenceFrance

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