Document Open Access Logo

Domination Problems in Nowhere-Dense Classes

Authors Anuj Dawar, Stephan Kreutzer

PDF

File

Thumbnail PDF
PDF
LIPIcs.FSTTCS.2009.2315.pdf
  • Filesize: 225 kB
  • 12 pages

Document Identifiers

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact