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

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 SecondOrder formulas.

• Type: Conference
• Year: 2005
• Where: CSL
• Authors: Bruno Courcelle, Christian Delhommé
• Keywords: CSL 2005, Modular Decompositions, Monadic Second-order Logic, Monadic SecondOrder Formulas