A graphon perspective for fractional isomorphism
Result 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.
Keywords
fractional isomorphismgraphonsdoubly stochastic operatorsmeasure disintegration theorem
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1236/724
DOI - Digital Object Identifier
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Alternative languages
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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Classification
Type
Jimp - 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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Mathematica Universitatis Comenianae
ISSN
0231-6986
e-ISSN
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Volume of the periodical
88
Issue of the periodical within the volume
3
Country of publishing house
SK - SLOVAKIA
Number of pages
7
Pages from-to
759-765
UT code for WoS article
000484349000063
EID of the result in the Scopus database
2-s2.0-85073774816
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2019