The modular decomposition of countable graphs: Constructions in monadic second-order logic

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. © Springer-Verlag Berlin Heidelberg 2005.