TY - JOUR
T1 - Radial Points in the Plane
AU - Pach, János
AU - Sharir, Micha
N1 - Funding Information:
Work on this paper has been supported by an NSF Grant CCR-97-32101, and by a grant from the U.S.–Israel Binational Science Foundation. Support has also been provided by OTKA T-020914 (JP) and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University (MS).
PY - 2001/8
Y1 - 2001/8
N2 - A radial point for a finite set P in the plane is a point q ∉ P with the property that each line connecting q to a point of P passes through at least one other element of P. We prove a conjecture of Pinchasi, by showing that the number of radial points for a non-collinear n-element set P is O(n). We also present several extensions of this result, generalizing theorems of Beck, Szemerédi and Trotter, and Elekes on the structure of incidences between points and lines.
AB - A radial point for a finite set P in the plane is a point q ∉ P with the property that each line connecting q to a point of P passes through at least one other element of P. We prove a conjecture of Pinchasi, by showing that the number of radial points for a non-collinear n-element set P is O(n). We also present several extensions of this result, generalizing theorems of Beck, Szemerédi and Trotter, and Elekes on the structure of incidences between points and lines.
UR - http://www.scopus.com/inward/record.url?scp=0035640107&partnerID=8YFLogxK
U2 - 10.1006/eujc.2001.0506
DO - 10.1006/eujc.2001.0506
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0035640107
VL - 22
SP - 855
EP - 863
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
IS - 6
ER -