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Domination Problems in Nowhere-Dense Classes Dawar, Anuj Kreutzer, Stephan Dominating Set distance-d dominating set nowhere-dense graph classes H-minor free graphs fixed-parameter tractablility 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anuj Dawar and Stephan Kreutzer 2009 Is Part Of LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2009.2315 urn:nbn:de:0030-drops-23153 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2315 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode