@article{4080,
abstract = {This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n12−112+O(1)n47 points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.},
author = {Herbert Edelsbrunner and Hasan, Nany and Seidel, Raimund and Shen, Xiao-Jun},
journal = {Geometriae Dedicata},
number = {1},
pages = {1 -- 12},
publisher = {Kluwer},
title = {{Circles through two points that always enclose many points}},
doi = {10.1007/BF00181432},
volume = {32},
year = {1989},
}