Centerpoints and Tverberg's technique

Using a technique that Tverberg and Vrecica [TV93] discovered to give a surprisingly simple proof of Tverberg's theorem, we show the following extension of the centerpoint theorem. Given any set P of n points in the plane, and a parameter 1/3 c 1, one can always find a disk D such that any closed half-space containing D contains at least cn points of P. Furthermore, D contains at most (3c - 1)n/2 points of P (the case c = 1 is trivial

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Abdul Basit, Nabil H. Mustafa, Saurabh Ray, Sarfraz Raza
• Keywords: Applied Computing, Closed Half-space, Cn Points, COMGEO 2010, Simple Proof