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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Matoušek, J. (2002). Transversals and Epsilon Nets. In: Matoušek, J. (eds) Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0039-7_10
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0039-7_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95374-8
Online ISBN: 978-1-4613-0039-7
eBook Packages: Springer Book Archive