2 research outputs found
On Polygons Excluding Point Sets
By a polygonization of a finite point set in the plane we understand a
simple polygon having as the set of its vertices. Let and be sets
of blue and red points, respectively, in the plane such that is in
general position, and the convex hull of contains interior blue points
and 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 . We show that there is a minimal number , which is
polynomial in , such that one can always find a blue polygonization
excluding all red points, whenever . Some other related problems are
also considered.Comment: 14 pages, 15 figure