Gadget Construction and Structural Convergence
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00635684" target="_blank" >RIV/67985807:_____/25:00635684 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/25:10496037
Result on the web
<a href="https://doi.org/10.1007/s00493-025-00140-8" target="_blank" >https://doi.org/10.1007/s00493-025-00140-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00493-025-00140-8" target="_blank" >10.1007/s00493-025-00140-8</a>
Alternative languages
Result language
angličtina
Original language name
Gadget Construction and Structural Convergence
Original language description
Nešetřil and Ossona de Mendez recently proposed a new definition of graph convergence called structural convergence. The structural convergence framework is based on the probability of satisfaction of logical formulas from a fixed fragment of first-order formulas. The flexibility of choosing the fragment allows to unify the classical notions of convergence for sparse and dense graphs. Since the field is relatively young, the range of examples of convergent sequences is limited and only a few methods of construction are known. Our aim is to extend the variety of constructions by considering the gadget construction. We show that, when restricting to the set of sentences, the application of gadget construction on elementarily convergent sequences yields an elementarily convergent sequence. On the other hand, we show counterexamples witnessing that a generalization to the full first-order convergence is not possible without additional assumptions. We give several different sufficient conditions to ensure the full convergence. One of them states that the resulting sequence is first-order convergent if the replaced edges are dense in the original sequence of structures.
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
Combinatorica
ISSN
0209-9683
e-ISSN
1439-6912
Volume of the periodical
45
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
35
Pages from-to
15
UT code for WoS article
001444705500002
EID of the result in the Scopus database
2-s2.0-105000163725