  We prove that for every nowhere dense class of graphs $\mathcal{C}$, positive
integer $d$, and $\varepsilon>0$, the following holds: in every $n$-vertex
graph $G$ from $\mathcal{C}$ one can find two disjoint vertex subsets
$A,B\subseteq V(G)$ such that $|A|\geq (1/2-\varepsilon)\cdot n$ and
$|B|=\Omega(n^{1-\varepsilon})$ and either $\operatorname{dist}(a,b)\leq d$ for
all $a\in A$ and $b\in B$, or $\operatorname{dist}(a,b)>d$ for all $a\in A$ and
$b\in B$. We also show some stronger variants of this statement, including a
generalization to the setting of First-Order interpretations of nowhere dense
graph classes.
