Abstract
A line L separates a set A from a collection S of plane sets if A is contained in one of the closed half-planes defined by L , while every set in S is contained in the complementary closed half-plane. Let ƒ( n ) be the largest integer such that for any collection F of n closed disks in the plane with pairwise disjoint interiors, there is a line that separates a disk in F from a subcollection of F with at least ƒ( n ) disks. In this note we prove that there is a constant c such that ƒ(n)⩾ (n − c) 2 . An analogous result for the d -dimensional Euclidean space is also discussed.
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