2022/10/25 by Jan Hladký, Eng Keat Hng
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Graph theory and applications
paper · pdf · doi:10.1016/j.ejc.2023.103751
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.