Topological Hypergraphs

Sarit Buzaglo (), Rom Pinchasi () and Günter Rote ()
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Sarit Buzaglo: Technion—Israel Institute of Technology, Mathematics Department
Rom Pinchasi: Technion—Israel Institute of Technology, Mathematics Department
Günter Rote: Freie Universität Berlin, Institut für Informatik

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 71-81 from Springer

Abstract: Abstract Let P be a set of n points in the plane. A topological hypergraphG, 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.

Keywords: Largest Cardinality; Graph Topology; Entire Edge; Planar Graphs (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_6

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DOI: 10.1007/978-1-4614-0110-0_6

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