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Communication Dans Un Congrès Année : 2021

Rankwidth meets stability

Jaroslav Nešetřil
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  • PersonId : 946576
Michał Pilipczuk
Roman Rabinovich
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  • PersonId : 1112963
Sebastian Siebertz
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  • PersonId : 1112964

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:
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Dates et versions

hal-03373553 , version 1 (11-10-2021)

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  • HAL Id : hal-03373553 , version 1

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Patrice Ossona de Mendez, Jaroslav Nešetřil, Michał Pilipczuk, Roman Rabinovich, Sebastian Siebertz. Rankwidth meets stability. Symposium on Discrete Algorithms (SODA), Jan 2021, Alexandria, United States. ⟨hal-03373553⟩

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