%A GrebĂk, Jan
%A Rocha, Israel
%D 2019
%T A graphon perspective for fractional isomorphism
%K
%X 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 Birkhoff\textendash von Neumann Theorem.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1236
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 759-765%V 88
%N 3
%@ 0862-9544
%8 2019-07-30