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Domination Problems in Nowhere-Dense Classes

Authors Anuj Dawar, Stephan Kreutzer

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LIPIcs.FSTTCS.2009.2315.pdf
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Keywords
  • Dominating Set
  • distance-d dominating set
  • nowhere-dense graph classes
  • H-minor free graphs
  • fixed-parameter tractablility

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Abstract

We investigate the parameterized complexity of generalisations and variations
of the dominating set problem on classes of graphs that are nowhere dense.  In
particular, we show that the distance-$d$ dominating-set problem, also known
as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that
is nowhere dense and closed under induced subgraphs.  This generalises known
results about the dominating set problem on $H$-minor free classes, classes
with locally excluded minors and classes of graphs of bounded expansion.  A
key feature of our proof is that it is based simply on the fact that these
graph classes are uniformly quasi-wide, and does not rely on a structural
decomposition.  Our result also establishes that the distance-$d$
dominating-set problem is FPT on classes of bounded expansion, answering a
question of Ne{\v s}et{\v r}il and Ossona de Mendez.

Cite As Get BibTex

Anuj Dawar and Stephan Kreutzer. Domination Problems in Nowhere-Dense Classes. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 157-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2315

Author Details

Anuj Dawar
Stephan Kreutzer
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