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