Algorithmica

, 61:971 | Cite as

Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three

  • Marwan Al-Jubeh
  • Mashhood Ishaque
  • Kristóf Rédei
  • Diane L. Souvaine
  • Csaba D. Tóth
  • Pavel Valtr
Article

Abstract

We characterize the planar straight line graphs (Pslgs) that can be augmented to 3-connected and 3-edge-connected Pslgs, respectively. We show that if a Pslg with n vertices can be augmented to a 3-edge-connected Pslg, then at most 2n−2 new edges are always sufficient and sometimes necessary for the augmentation. If the input Pslg is, in addition, already 2-edge-connected, then n−2 new edges are always sufficient and sometimes necessary for the augmentation to a 3-edge-connected Pslg.

Keywords

Connectivity augmentation Planar straight line graph Graph embedding 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Marwan Al-Jubeh
    • 1
  • Mashhood Ishaque
    • 1
  • Kristóf Rédei
    • 1
  • Diane L. Souvaine
    • 1
  • Csaba D. Tóth
    • 2
  • Pavel Valtr
    • 3
  1. 1.Department of Computer ScienceTufts UniversityMedfordUSA
  2. 2.Department of MathematicsUniversity of CalgaryCalgaryCanada
  3. 3.Department of Applied Mathematics and Institute for Theoretical Computer ScienceCharles UniversityPragueCzech Republic

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