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Disjoint Edges in Topological Graphs

  • János Pach
  • Géza Tóth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

A topological graph G is a graph drawn in the plane so that its edges are represented by Jordan arcs. G is called simple, if any two edges have at most one point in common. It is shown that the maximum number of edges of a simple topological graph with n vertices and no k pairwise disjoint edges is O(nlog4k − 8 n) edges. The assumption that G is simple cannot be dropped: for every n, there exists a complete topological graph of n vertices, whose any two edges cross at most twice.

Keywords

Computational Geometry Topological Graph Geometric Graph London Mathematical Society Lecture Note Disjoint Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • János Pach
    • 1
  • Géza Tóth
    • 2
  1. 1.City College, CUNY and Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Rényi Institute of the Hungarian Academy of SciencesBudapestHungary

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