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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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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)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Article name in the collection

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

ISBN

978-80-280-0344-9

ISSN

2788-3116

e-ISSN

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Number of pages

7

Pages from-to

216-222

Publisher name

Masaryk University Press

Place of publication

Masaryk University, Brno

Event location

Praha

Event date

Aug 28, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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