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∪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≥K. Some other related problems are
also considered.Comment: 14 pages, 15 figure