On polygons excluding point sets

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 a 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.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Radoslav Fulek, Balázs Keszegh, Filip Moric, Igor Uljarevic
• Keywords: Blue Polygonization, CCCG 2010, Computational Geometry, Interior Blue Points, Red Points