Rankwidth meets stability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438592" target="_blank" >RIV/00216208:11320/21:10438592 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/1.9781611976465.120" target="_blank" >https://doi.org/10.1137/1.9781611976465.120</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/1.9781611976465.120" target="_blank" >10.1137/1.9781611976465.120</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rankwidth meets stability

Popis výsledku v původním jazyce

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 define arbitrarily long linear orders in vertex-colored graphs from C using a fixed first-order formula. Similarly, monadic dependence corresponds to the impossibility of defining 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. Thus, 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: 1) A class of graphs C is a first-order transduction of a class with bounded treewidth if and only if C has bounded rankwidth and a stable edge relation (i.e. graphs from C exclude some half-graph as a semi-induced subgraph). 2) If a class of graphs C is monadically dependent and not monadically stable, then C has in fact an unstable edge relation. As a consequence, we show that classes with bounded rankwidth excluding some half-graph as a semi-induced subgraph are linearly χ-bounded. Our proofs are effective and lead to polynomial time algorithms.

Název v anglickém jazyce

Rankwidth meets stability

Popis výsledku anglicky

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 define arbitrarily long linear orders in vertex-colored graphs from C using a fixed first-order formula. Similarly, monadic dependence corresponds to the impossibility of defining 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. Thus, 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: 1) A class of graphs C is a first-order transduction of a class with bounded treewidth if and only if C has bounded rankwidth and a stable edge relation (i.e. graphs from C exclude some half-graph as a semi-induced subgraph). 2) If a class of graphs C is monadically dependent and not monadically stable, then C has in fact an unstable edge relation. As a consequence, we show that classes with bounded rankwidth excluding some half-graph as a semi-induced subgraph are linearly χ-bounded. Our proofs are effective and lead to polynomial time algorithms.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ISBN

978-1-61197-646-5

ISSN

—

e-ISSN

—

Počet stran výsledku

20

Strana od-do

2014-2033

Název nakladatele

Association for Computing Machinery

Místo vydání

Neuveden

Místo konání akce

Online

Datum konání akce

10. 1. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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