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Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three

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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.

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Authors and Affiliations

  1. Department of Computer Science, Tufts University, Medford, MA, USA

    Marwan Al-Jubeh, Mashhood Ishaque, Kristóf Rédei & Diane L. Souvaine

  2. Department of Mathematics, University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

  3. Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Prague, Czech Republic

    Pavel Valtr

Authors
  1. Marwan Al-Jubeh
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  2. Mashhood Ishaque
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  3. Kristóf Rédei
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  4. Diane L. Souvaine
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  5. Csaba D. Tóth
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  6. Pavel Valtr
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Corresponding author

Correspondence to Csaba D. Tóth.

Additional information

M.A.-J., M.I., K.R., D.L.S., C.D.T. were partially supported by NSF grant CCF-0830734.

Research by C.D. Tóth was conducted while visiting the Rényi Institute, Budapest, and Tufts University, Medford, MA. Supported in part by NSERC grant RGPIN 35586.

Research by P. Valtr was supported by the projects 1M0545 and MSM0021620838 of the Ministry of Education of the Czech Republic.

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Al-Jubeh, M., Ishaque, M., Rédei, K. et al. Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three. Algorithmica 61, 971–999 (2011). https://doi.org/10.1007/s00453-011-9551-0

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  • DOI: https://doi.org/10.1007/s00453-011-9551-0

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