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.MFCS.2019.41
URN: urn:nbn:de:0030-drops-109856
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10985/
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Galby, Esther ; Lima, Paloma T. ; Ries, Bernard

Reducing the Domination Number of Graphs via Edge Contractions

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LIPIcs-MFCS-2019-41.pdf (0.5 MB)

Abstract

In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that it remains NP-hard when restricted to P_9-free graphs, bipartite graphs and {C_3,...,C_{l}}-free graphs for any l >= 3. Finally, we show that for any k >= 1, the problem is polynomial-time solvable for P_5-free graphs and that it can be solved in FPT-time and XP-time when parameterized by tree-width and mim-width, respectively.

BibTeX - Entry

@InProceedings{galby_et_al:LIPIcs:2019:10985,
  author =	{Esther Galby and Paloma T. Lima and Bernard Ries},
  title =	{{Reducing the Domination Number of Graphs via Edge Contractions}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{41:1--41:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10985},
  URN =		{urn:nbn:de:0030-drops-109856},
  doi =		{10.4230/LIPIcs.MFCS.2019.41},
  annote =	{Keywords: domination number, blocker problem, graph classes}
}

Keywords: domination number, blocker problem, graph classes
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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