Unavoidable Configurations in Complete Topological Graphs

  • János Pach
  • Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)

Abstract

A topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by Jordan curves connecting the corresponding points, with the property that any two curves have at most one point in common. We define two canonical classes of topological complete graphs, and prove that every topological complete graph with n vertices has a canonical subgraph of size at least c log log n, which belongs to one of these classes. We also show that every complete topological graph with n vertices has a non- crossing subgraph isomorphic to any fixed tree with at most c log1/6 n vertices.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • János Pach
    • 1
  • Géza Tóth
    • 2
  1. 1.NYU and Hungarian Academy of SciencesCourant InstituteHungary
  2. 2.Massachusetts Institute of Technology and Hungarian Academy of SciencesHungary

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