License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.33
URN: urn:nbn:de:0030-drops-85140
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8514/
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Ganian, Robert ; Klute, Fabian ; Ordyniak, Sebastian

On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

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Abstract

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve the main open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number.

BibTeX - Entry

@InProceedings{ganian_et_al:LIPIcs:2018:8514,
  author =	{Robert Ganian and Fabian Klute and Sebastian Ordyniak},
  title =	{{On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8514},
  URN =		{urn:nbn:de:0030-drops-85140},
  doi =		{10.4230/LIPIcs.STACS.2018.33},
  annote =	{Keywords: bounded-degree vertex deletion, feedback vertex set, parameterized algorithms, treecut width}
}

Keywords: bounded-degree vertex deletion, feedback vertex set, parameterized algorithms, treecut width
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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