Graph drawing with no k pairwise crossing edges

  • Pavel Valtr
Crossings and Planarity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

A geometric graph is a graph G = (V, E) drawn in the plane so that the vertex set V consists of points in general position and the edge set E consists of straight line segments between points of V. It is known that, for any fixed k, any geometric graph G on n vertices with no k pairwise crossing edges contains at most O(n log n) edges. In this paper we give a new, simpler proof of this bound, and show that the same bound holds also when the edges of G are represented by x-monotone curves (Jordan arcs).

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Pavel Valtr
    • 1
    • 2
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic
  2. 2.DIMACS CenterRutgers UniversityPiscatawayUSA

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