Rooting algebraic vertices of convergent sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00573756" target="_blank" >RIV/67985807:_____/23:00573756 - isvavai.cz</a>
Result on the web
<a href="https://journals.phil.muni.cz/eurocomb/article/view/35609/31523" target="_blank" >https://journals.phil.muni.cz/eurocomb/article/view/35609/31523</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>

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 (Gn) converging to a limit L and a vertex r of L it is possible to find a sequence of vertices (rn) such that L rooted at r is the limit of the graphs Gn rooted at rn. A counterexample was found by Christofides and Král’, but they showed that the statement holds for almost all vertices r 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 r is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots (rn) always exists.
Czech name
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Czech description
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Project
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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
EUROCOMB’23. Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications
ISBN
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ISSN
2788-3116
e-ISSN
2788-3116
Number of pages
6
Pages from-to
539-544
Publisher name
MUNI Press
Place of publication
Brno
Event location
Prague
Event date
Aug 28, 2023
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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