Rankwidth meets stability
Résumé
We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs C is monadically stable if it is impossible to de ne arbitrarily long linear orders in vertex-colored graphs from C using a xed rst-order formula. Similarly, monadic dependence corresponds to the impossibility of de ning all graphs in this way. Examples of monadically stable graph classes are nowhere dense classes, which provide a robust theory of sparsity. Examples of monadically dependent classes are classes of bounded rankwidth (or equivalently, bounded cliquewidth), which can be seen as a dense analog of classes of bounded treewidth. us, monadic stability and monadic dependence extend classical structural notions for graphs by viewing them in a wider, model-theoretical context. We explore this emerging theory by proving the following:
Domaines
Combinatoire [math.CO]
Origine : Fichiers produits par l'(les) auteur(s)