Lovász–Szegedy finite-dimensionality conjecture for finitely forcible graphons

A graphon is an analytic representation of the limit of a convergent sequence of dense graphs; a graphon is finitely forcible if it is uniquely determined, up to isomorphism, by finitely many graph densities. The space of typical vertices is the vertex space associated with a graphon and its graph-limit structure.

Lovász–Szegedy finite-dimensionality conjecture. The space of typical vertices of every finitely forcible graphon has finite dimension.

Lovász and Szegedy proposed this as a formalization of the expectation that finitely forcible graphons have a simple structure. The conjecture was disproved by counterexample constructions.