A graphon perspective for fractional isomorphism

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00508686" target="_blank" >RIV/67985807:_____/19:00508686 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1236/724" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1236/724</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A graphon perspective for fractional isomorphism
Original language description
Fractional isomorphism of graphs plays an important role in practical applications of graph isomorphism test by means of the color refinement algorithm. We introduce a suitable generalization to the space of graphons in terms of Markov opertors on a Hilbert space, provide characterizations in terms of a push-forward of the graphon to a quotient space and also in terms of measurable partitions of the underlying space. Our proofs use a weak version of the mean ergodic theorem, and correspondences between objects such as Markov projections, sub-$sigma$-algebras, measurable decompositions, etc. That also provides an alternative proof for the characterizations of fractional isomorphism of graphs without the use of Birkhofftextendash von Neumann Theorem.
Czech name
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Czech description
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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

Project
<a href="/en/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremal graph theory and applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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