Nowhere dense graph classes provide one of the least restrictive notions of
sparsity for graphs. Several equivalent characterizations of nowhere dense
classes have been obtained over the years, using a wide range of combinatorial
objects. In this paper we establish a new characterization of nowhere dense
classes, in terms of poset dimension: A monotone graph class is nowhere dense
if and only if for every h≥1 and every ϵ>0, posets of height
at most h with n elements and whose cover graphs are in the class have
dimension O(nϵ).Comment: v4: Minor changes suggested by a refere