Rooting algebraic vertices of convergent sequences
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10477028" target="_blank" >RIV/00216208:11320/23:10477028 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-075" target="_blank" >https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-075</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5817/CZ.MUNI.EUROCOMB23-075" target="_blank" >10.5817/CZ.MUNI.EUROCOMB23-075</a>
Alternative languages
Result language
angličtina
Original language name
Rooting algebraic vertices of convergent sequences
Original language description
Structural convergence is a framework for convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence.They posed a problem asking whether for a given sequence of graphs G_n converging to a limit L and a vertex r of it is possible to find a sequence of vertices r_n such that L rooted at r is the limit of the graphs G_n rooted at r_n. A counterexample was found by Christofides and Král', but they showed that the statement holds for almost all vertices of L. We offer another perspective to the original problem by considering the size of definable sets to which the root r belongs. We prove that if is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots always exists.
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
2023
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 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
6
Pages from-to
539-544
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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