Fractionally Isomorphic Graphs and Graphons
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00583814" target="_blank" >RIV/67985807:_____/23:00583814 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-080" target="_blank" >https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-080</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5817/CZ.MUNI.EUROCOMB23-080" target="_blank" >10.5817/CZ.MUNI.EUROCOMB23-080</a>
Alternative languages
Result language
angličtina
Original language name
Fractionally Isomorphic Graphs and Graphons
Original language description
Fractional isomorphism is a well-studied relaxation of graph isomorphism with a very rich theory. Grebík and Rocha [Combinatorica 42, pp 365–404 (2022)] developed a concept of fractional isomorphism for graphons and proved that it enjoys an analogous theory. In particular, they proved that if two sequences of graphs that are fractionally isomorphic converge to two graphons, then these graphons are fractionally isomorphism. Answering the main question from ibid, we prove the converse of the statement above: If we have two fractionally isomorphic graphons, then there exist sequences of graphs that are fractionally isomorphic converge and converge to these respective graphons. As an easy but convenient corollary of our methods, we get that every regular graphon can be approximated by regular graphs.
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX21-21762X" target="_blank" >GX21-21762X: Graph limits and beyond</a><br>
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
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
8
Pages from-to
579-586
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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