Fundamental study: The modular decomposition of countable graphs. Definition and construction in monadic second-order logic

Authors:
Bruno Courcelle;Christian Delhommé
Affiliations:
Université Bordeaux 1 and Institut Universitaire de France, LaBRI (CNRS), 351 Cours de la Libération, F-33405 Talence, France;ERMIT, Université de La Réunion, 15, Avenue René Cassin, BP 7151, F-97715, Saint-Denis, Messag. cedex 9, La Réunion, France
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

We consider the notion of modular decomposition for countable graphs. The modular decomposition of a graph given with an enumeration of its set of vertices can be defined by formulas of monadic second-order logic. Another result is the definition of a representation of modular decompositions by low degree relational structures. Such relational structures can also be defined in the considered graph by monadic second-order formulas.