Approximating fractionally isomorphic graphons

0570704 - ÚI 2024 US eng V - Research Report
Hladký, Jan - Hng, Eng Keat
Approximating fractionally isomorphic graphons.
Cornell University: Cornell University, 2023. 22 s. arXiv.org e-Print archive, 2210.14097.
R&D Projects: GA ČR(CZ) GA22-01137S
Institutional support: RVO:67985807
https://arxiv.org/abs/2210.14097

Grebík 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.
Permanent Link: https://hdl.handle.net/11104/0342029