  Inspired by Adler's idea on VC minimal theories \cite{adler2008theories}, we
introduce VC-minimal complexity. We show that for any $N\in\mathbb{N}^{>0}$,
there is $k_N>0$ such that for any finite bipartite graph $(X,Y;E)$ with
VC-minimal complexity $< N$, there exist $X'\subseteq X$, $Y'\subseteq Y$ with
$|X'|\geq k_N |X|$, $|Y'|\geq k_N |Y|$ such that $X'\times Y' \subseteq E$ or
$X'\times Y'\cap E=\emptyset$.
