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.
|Number of pages||4|
|State||Published - 2010|
|Event||22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 - Winnipeg, MB, Canada|
Duration: 9 Aug 2010 → 11 Aug 2010
|Conference||22nd Annual Canadian Conference on Computational Geometry, CCCG 2010|
|Period||9/08/10 → 11/08/10|