## Sarit Buzaglo, Rom Pinchasi, and Günter Rote:

# Topological hypergraphs

In: *Thirty Essays on Geometric Graph Theory*. Editor: János
Pach, Springer-Verlag, 2013, pp. 71–81. doi:10.1007/978-1-4614-0110-0_6*
*
### Abstract

Let `P` be a set of `n` points in the plane. A topological
hypergraph `G` on the set of points of `P` is a collection
of simple closed curves in the plane that avoid the points of `P`.
Each of these curves is called an edge of `G`, and the points of
`P` are called the vertices of `G`. We provide bounds on the
number of edges of topological hypergraphs in terms of the number of their
vertices under various restrictions assuming the set of edges is a family of
pseudo-circles.

Last update: October 24, 2013.