Compressing Bounded Degree Graphs

  • Pål Grønås Drange
  • Markus DregiEmail author
  • R. B. Sandeep
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)


Recently, Aravind et al. (IPEC 2014) showed that for any finite set of connected graphs \(\mathcal {H}\), the problem \(\mathcal {H}\)-Free Edge Deletion admits a polynomial kernelization on bounded degree input graphs. We generalize this theorem by no longer requiring the graphs in \(\mathcal {H}\) to be connected. Furthermore, we complement this result by showing that also \(\mathcal {H}\)-Free Edge Editing admits a polynomial kernelization on bounded degree input graphs.

We show that there exists a finite set \(\mathcal {H}\) of connected graphs such that \(\mathcal {H}\)-Free Edge Completion is incompressible even on input graphs of maximum degree 5, unless the polynomial hierarchy collapses to the third level. Under the same assumption, we show that \(C_{11}\) -free Edge Deletion—as well as \(\mathcal {H}\)-Free Edge Editing—is incompressible on 2-degenerate graphs.


Connected Graph Maximum Degree Input Graph Polynomial Kernel Free Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Pål Grønås Drange
    • 1
  • Markus Dregi
    • 1
    Email author
  • R. B. Sandeep
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Department of CSEIIT HyderabadMedakIndia

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