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Small Point Sets for Simply-Nested Planar Graphs

  • Patrizio Angelini
  • Giuseppe Di Battista
  • Michael Kaufmann
  • Tamara Mchedlidze
  • Vincenzo Roselli
  • Claudio Squarcella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Abstract

A point set P ⊆ ℝ2 is universal for a class \(\cal G\) if every graph of \({\cal G}\) has a planar straight-line embedding into P. We prove that there exists a \(O(n (\frac{\log n}{\log\log n})^2)\) size universal point set for the class of simply-nested n-vertex planar graphs. This is a step towards a full answer for the well-known open problem on the size of the smallest universal point sets for planar graphs [1, 5, 9].

Keywords

Planar Graph Dense Level Sparse Level Cardinal Point Planar Triangulation 
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

  • Patrizio Angelini
    • 1
  • Giuseppe Di Battista
    • 1
  • Michael Kaufmann
    • 2
  • Tamara Mchedlidze
    • 3
  • Vincenzo Roselli
    • 1
  • Claudio Squarcella
    • 1
  1. 1.Dip. di Informatica e AutomazioneRoma Tre UniversityItaly
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  3. 3.Dept. of Math.National Technical University of AthensGreece

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