Disjoint Edges in Topological Graphs

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


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.


Computational Geometry Topological Graph Geometric Graph London Mathematical Society Lecture Note Disjoint Edge 
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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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