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Upper Bound Constructions for Untangling Planar Geometric Graphs

  • Javier Cano
  • Csaba D. Tóth
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Abstract

For every n ∈ ℕ, there is a straight-line drawing D n of a planar graph on n vertices such that in any crossing-free straight-line drawing of the graph, at most O(n .4982) vertices lie at the same position as in D n . This improves on an earlier bound of \(O(\sqrt{n})\) by Goaoc et al. [6].

Keywords

Planar Graph Jordan Curve Outer Face Interior Vertex Marked Vertex 
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 2012

Authors and Affiliations

  • Javier Cano
    • 1
  • Csaba D. Tóth
    • 2
  • Jorge Urrutia
    • 3
  1. 1.Posgrado en Ciencia e Ingeniería de la ComputaciónUniversidad Nacional Autónoma de MéxicoMéxico
  2. 2.Department of Math.University of CalgaryCanada
  3. 3.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMéxico

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