Approximating fractionally isomorphic graphons
Combinatorics
2023-09-22 v2
Abstract
Greb\'ik and Rocha [Fractional Isomorphism of Graphons, Combinatorica 42, pp 365-404 (2022)] extended the well studied notion of fractional isomorphism of graphs to graphons. We prove that fractionally isomorphic graphons can be approximated in the cut distance by fractionally isomorphic finite graphs. This answers the main question from ibid. As an easy but convenient corollary, we deduce that every regular graphon can be approximated by regular graphs.
Cite
@article{arxiv.2210.14097,
title = {Approximating fractionally isomorphic graphons},
author = {Jan Hladký and Eng Keat Hng},
journal= {arXiv preprint arXiv:2210.14097},
year = {2023}
}
Comments
23 pages, 2 figures; as will appear in European Journal of Combinatorics