TY - JOUR
AB - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(c log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.
AU - Aronov, Boris
AU - Chazelle, Bernard
AU - Edelsbrunner, Herbert
AU - Guibas, Leonidas
AU - Sharir, Micha
AU - Wenger, Rephael
ID - 4062
IS - 1
JF - Discrete & Computational Geometry
SN - 0179-5376
TI - Points and triangles in the plane and halving planes in space
VL - 6
ER -