Decomposition horizons: from graph sparsity to model-theoretic dividing lines

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10477017" target="_blank" >RIV/00216208:11320/23:10477017 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-030" target="_blank" >https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-030</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5817/CZ.MUNI.EUROCOMB23-030" target="_blank" >10.5817/CZ.MUNI.EUROCOMB23-030</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Decomposition horizons: from graph sparsity to model-theoretic dividing lines

Popis výsledku v původním jazyce

Low treedepth decompositions are central to the structural characterizations of bounded expansion classes and nowhere dense classes, and the core of main algorithmic properties of these classes, including fixed-parameter (quasi) linear-time algorithms checking whether a fixed graph is an induced subgraph of the input graph. These decompositions have been extended to structurally bounded expansion classes and structurally nowhere dense classes, where low treedepth decompositions are replaced by low shrubdepth decompositions. In the emerging framework of a structural graph theory for hereditary classes of structures based on tools from model theory, it is natural to ask how these decompositions behave with the fundamental model theoretical notions of dependence (alias NIP) and stability. In this work, we prove that the model theoretical notions of NIP and stable classes are transported by decompositions.

Název v anglickém jazyce

Decomposition horizons: from graph sparsity to model-theoretic dividing lines

Popis výsledku anglicky

Low treedepth decompositions are central to the structural characterizations of bounded expansion classes and nowhere dense classes, and the core of main algorithmic properties of these classes, including fixed-parameter (quasi) linear-time algorithms checking whether a fixed graph is an induced subgraph of the input graph. These decompositions have been extended to structurally bounded expansion classes and structurally nowhere dense classes, where low treedepth decompositions are replaced by low shrubdepth decompositions. In the emerging framework of a structural graph theory for hereditary classes of structures based on tools from model theory, it is natural to ask how these decompositions behave with the fundamental model theoretical notions of dependence (alias NIP) and stability. In this work, we prove that the model theoretical notions of NIP and stable classes are transported by decompositions.

Druh

D - Stať ve sborníku

CEP obor

—

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

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications

ISBN

978-80-280-0344-9

ISSN

2788-3116

e-ISSN

—

Počet stran výsledku

7

Strana od-do

216-222

Název nakladatele

Masaryk University Press

Místo vydání

Masaryk University, Brno

Místo konání akce

Praha

Datum konání akce

28. 8. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—