Lectures on Discrete Geometry pp 231-263 | Cite as

# Transversals and Epsilon Nets

## Abstract

Here we are going to consider problems of the following type: We have a family *F* of geometric shapes satisfying certain conditions, and we would like to conclude that *F* can be “pierced” by not too many points, meaning that we can choose a bounded number of points such that each set of *F* contains at least one of them. Such questions are sometimes called *Gallai-type problems*, because of the following nice problem raised by Gallai: Let *F* be a finite family of closed disks in the plane such that every two disks in *F* intersect. What is the smallest number of points needed to pierce *F* For this problem, the exact answer is known: 4 points always suffice and are sometimes necessary.

### Keywords

Radon Lution Suffix## Preview

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