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


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.

other papers about this subject
Last update: October 24, 2013.