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].

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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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