Projects per year
Abstract
Let S be a kcolored (finite) set of n points in Rd, d≥3, in general position, that is, no (d+1) points of S lie in a common (d−1)dimensional hyperplane. We count the number of empty monochromatic dsimplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3≤k≤d we provide a lower bound of Ω(nd−k+1+2−d)
and strengthen this to Ω(n d−2/3) for k=2.
On the way we provide various results on triangulations of point sets in Rd
. In particular, for any constant dimension d≥3, we prove that every set of n points (n sufficiently large), in general position in Rd, admits a triangulation with at least dn+Ω(logn) simplices.
and strengthen this to Ω(n d−2/3) for k=2.
On the way we provide various results on triangulations of point sets in Rd
. In particular, for any constant dimension d≥3, we prove that every set of n points (n sufficiently large), in general position in Rd, admits a triangulation with at least dn+Ω(logn) simplices.
Original language  English 

Pages (fromto)  362393 
Journal  Discrete & Computational Geometry 
Volume  52 
Issue number  2 
DOIs  
Publication status  Published  2014 
Fields of Expertise
 Information, Communication & Computing
Treatment code (Nähere Zuordnung)
 Theoretical

Discrete and Computational Geometry
Hackl, T., Aigner, W., Pilz, A., Vogtenhuber, B., Kornberger, B. & Aichholzer, O.
1/01/05 → …
Project: Research area

FWF  ComPoSe  EuroGIAG_ErdösSzekeres type problems for colored point sets and compatible graphs
1/10/11 → 31/12/15
Project: Research project

FWF  CPGG  Combinatorial Problems on Geometric Graphs
Hackl, T.
1/09/11 → 31/12/15
Project: Research project