  By a polygonization of a finite point set $S$ in the plane we understand a
simple polygon having $S$ as the set of its vertices. Let $B$ and $R$ be sets
of blue and red points, respectively, in the plane such that $B\cup R$ is in
general position, and the convex hull of $B$ contains $k$ interior blue points
and $l$ interior red points. Hurtado et al. found sufficient conditions for the
existence of a blue polygonization that encloses all red points. We consider
the dual question of the existence of a blue polygonization that excludes all
red points $R$. We show that there is a minimal number $K=K(l)$, which is
polynomial in $l$, such that one can always find a blue polygonization
excluding all red points, whenever $k\geq K$. Some other related problems are
also considered.
