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LATIN 2016: Theoretical Informatics

LATIN 2016: LATIN 2016: Theoretical Informatics pp 362–375Cite as

Compressing Bounded Degree Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9644))

Abstract

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.

The research leading to these results has received funding from the TCS Research Scholarship, Bergen Research Foundation under the project Beating Hardness by Preprocessing and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 267959.

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Notes

  1. 1.

    \({\textsf {NP}} \subseteq {\textsf {coNP/poly}}\) implies that PH is contained in \(\varSigma ^p_3\). It is widely believed that PH does not collapse, and hence it is also believed that \({\textsf {NP}} \not \subseteq {\textsf {coNP/poly}}\). We will throughout this section assume that \({\textsf {NP}} \not \subseteq {\textsf {coNP/poly}}\).

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Pål Grønås Drange & Markus Dregi

  2. Department of CSE, IIT Hyderabad, Medak, India

    R. B. Sandeep

Authors
  1. Pål Grønås Drange
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  2. Markus Dregi
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  3. R. B. Sandeep
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Corresponding author

Correspondence to Markus Dregi .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, ON, Ontario, Canada

    Evangelos Kranakis

  2. University Chile, Santiago, Chile

    Gonzalo Navarro

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Drange, P.G., Dregi, M., Sandeep, R.B. (2016). Compressing Bounded Degree Graphs. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_27

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  • DOI: https://doi.org/10.1007/978-3-662-49529-2_27

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  • Print ISBN: 978-3-662-49528-5

  • Online ISBN: 978-3-662-49529-2

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