Abstract
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.
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Courcelle, B., Delhommé, C. (2005). The Modular Decomposition of Countable Graphs: Constructions in Monadic Second-Order Logic. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_23
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DOI: https://doi.org/10.1007/11538363_23
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