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Topological Hypergraphs

In: Thirty Essays on Geometric Graph Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sarit Buzaglo & Rom Pinchasi & Günter Rote, 2013. "Topological Hypergraphs," Springer Books, in: János Pach (ed.), Thirty Essays on Geometric Graph Theory, pages 71-81, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-0110-0_6
    DOI: 10.1007/978-1-4614-0110-0_6
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