Title: Approximating fractionally isomorphic graphons

Abstract: Fractional isomorphism of finite graphs is an important and
well-studied concept at the intersection of graph theory and
combinatorial optimization. It has many different characterizations that
involve a range of very different and seemingly unrelated properties of
graphs. Recently, Grebík and Rocha developed a theory of fractional
isomorphism for graphons, i.e. limits of dense graph sequences, where
they showed that every characterization of fractional isomorphism in
graphs has a well-defined graphon counterpart and that these are indeed
all equivalent characterizations of fractional isomorphism for graphons.
They asked whether fractionally isomorphic graphons can be characterized
as the limits of graph sequences which are entrywise fractionally
isomorphic (in the graph sense). We answer their question in the
affirmative.

This is joint work with Jan Hladký.