Structural convergence and algebraic roots
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00604104" target="_blank" >RIV/67985807:_____/25:00604104 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/24:10490830
Result on the web
<a href="https://doi.org/10.1017/S0963548324000427" target="_blank" >https://doi.org/10.1017/S0963548324000427</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0963548324000427" target="_blank" >10.1017/S0963548324000427</a>
Alternative languages
Result language
angličtina
Original language name
Structural convergence and algebraic roots
Original language description
Structural convergence is a framework for the 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 on 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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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Combinatorics Probability & Computing
ISSN
0963-5483
e-ISSN
1469-2163
Volume of the periodical
34
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
9
Pages from-to
392-400
UT code for WoS article
001382656200001
EID of the result in the Scopus database
2-s2.0-85213876386