文章基本信息

标题：Domination Problems in Nowhere-Dense Classes
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作者：Anuj Dawar ; Stephan Kreutzer
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：4
页码：157-168
DOI：10.4230/LIPIcs.FSTTCS.2009.2315
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Dominating Set; distance-d dominating set; nowhere-dense graph classes; H-minor free graphs; fixed-parameter tractablility