Nešetřil–Ossona de Mendez strong mass-transport conjecture for nowhere-dense classes

Let ${\cal C}$ be a nowhere-dense monotone class of graphs. A sequence of graphs from ${\cal C}$ is first-order convergent when the densities of tuples satisfying every first-order property converge. A modeling limit is an analytic limit object associated with such a sequence, and the strong finitary mass transport principle is the measure-theoretic condition imposed on sparse modeling limits.

Nešetřil–Ossona de Mendez's strong mass-transport conjecture. Every first-order convergent sequence of graphs from ${\cal C}$ has a modeling limit that satisfies the strong finitary mass transport principle.

The existence of a modeling limit for first-order convergent sequences from a monotone class is characterized by nowhere-denseness, but that result does not control measures of corresponding vertex subsets. This conjecture asks for the stronger mass-transport property and remains open in the supplied source.