Fractional Isomorphism of Graphons

2019/09/09 by Jan Grebík, Grebík, Jan, Israel Rocha +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1909.04122

openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is characterized in terms of distributions on iterated degree measures, Markov operators, weak isomorphism of a conditional expectation with respect to invariant sub-σ-algebras and isomorphism of certain quotients of given graphons.

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