@article{4062,
abstract = {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.},
author = {Aronov, Boris and Chazelle, Bernard and Herbert Edelsbrunner and Guibas, Leonidas J and Sharir, Micha and Wenger, Rephael},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {435 -- 442},
publisher = {Springer},
title = {{Points and triangles in the plane and halving planes in space}},
doi = {10.1007/BF02574700},
volume = {6},
year = {1991},
}