Rankwidth meets stability
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Rankwidth meets stability
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
ISBN
978-1-61197-646-5
ISSN
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e-ISSN
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Number of pages
20
Pages from-to
2014-2033
Publisher name
Association for Computing Machinery
Place of publication
Neuveden
Event location
Online
Event date
Jan 10, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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