Upward Geometric Graph Embeddings into Point Sets

  • Patrizio Angelini
  • Fabrizio Frati
  • Markus Geyer
  • Michael Kaufmann
  • Tamara Mchedlidze
  • Antonios Symvonis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)

Abstract

We study the problem of characterizing the directed graphs with an upward straight-line embedding into every point set in general or in convex position. We solve two questions posed by Binucci et al. [Computational Geometry: Theory and Applications, 2010]. Namely, we prove that the classes of directed graphs with an upward straight-line embedding into every point set in convex position and with an upward straight-line embedding into every point set in general position do not coincide, and we prove that every directed caterpillar admits an upward straight-line embedding into every point set in convex position. Further, we provide new partial positive results on the problem of constructing upward straight-line embeddings of directed paths into point sets in general position.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Fabrizio Frati
    • 1
  • Markus Geyer
    • 2
  • Michael Kaufmann
    • 2
  • Tamara Mchedlidze
    • 3
  • Antonios Symvonis
    • 3
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  3. 3.Dept. of MathematicsNational Technical University of AthensAthensGreece

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