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.ISAAC.2019.21
URN: urn:nbn:de:0030-drops-115171
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11517/
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Galby, Esther ; Lima, Paloma T. ; Ries, Bernard

Blocking Dominating Sets for H-Free Graphs via Edge Contractions

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LIPIcs-ISAAC-2019-21.pdf (0.5 MB)

Abstract

In this paper, we consider the following problem: given a connected graph G, can we reduce the domination number of G by one by using only one edge contraction? We show that the problem is NP-hard when restricted to {P_6,P_4+P_2}-free graphs and that it is coNP-hard when restricted to subcubic claw-free graphs and 2P_3-free graphs. As a consequence, we are able to establish a complexity dichotomy for the problem on H-free graphs when H is connected.

BibTeX - Entry

@InProceedings{galby_et_al:LIPIcs:2019:11517,
  author =	{Esther Galby and Paloma T. Lima and Bernard Ries},
  title =	{{Blocking Dominating Sets for H-Free Graphs via Edge Contractions}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11517},
  URN =		{urn:nbn:de:0030-drops-115171},
  doi =		{10.4230/LIPIcs.ISAAC.2019.21},
  annote =	{Keywords: domination number, blocker problem, H-free graphs}
}

Keywords: domination number, blocker problem, H-free graphs
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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