License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.MFCS.2020.64
URN: urn:nbn:de:0030-drops-127346
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12734/
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Lima, Paloma T. ; dos Santos, Vinicius F. ; Sau, Ignasi ; Souza, Uéverton S.

Reducing Graph Transversals via Edge Contractions

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LIPIcs-MFCS-2020-64.pdf (0.8 MB)

Abstract

For a graph parameter π, the Contraction(π) problem consists in, given a graph G and two positive integers k,d, deciding whether one can contract at most k edges of G to obtain a graph in which π has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where π is the size of a minimum dominating set. We focus on graph parameters defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection ℋ according to a fixed containment relation. We prove co-NP-hardness results under some assumptions on the graphs in ℋ, which in particular imply that Contraction(π) is co-NP-hard even for fixed k = d = 1 when π is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.

BibTeX - Entry

@InProceedings{lima_et_al:LIPIcs:2020:12734,
  author =	{Paloma T. Lima and Vinicius F. dos Santos and Ignasi Sau and U{\'e}verton S. Souza},
  title =	{{Reducing Graph Transversals via Edge Contractions}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{64:1--64:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12734},
  URN =		{urn:nbn:de:0030-drops-127346},
  doi =		{10.4230/LIPIcs.MFCS.2020.64},
  annote =	{Keywords: blocker problem, edge contraction, graph transversal, parameterized complexity, vertex cover, feedback vertex set, odd cycle transversal}
}

Keywords: blocker problem, edge contraction, graph transversal, parameterized complexity, vertex cover, feedback vertex set, odd cycle transversal
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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