非稠密图类中的控制问题
Domination Problems in Nowhere-Dense Classes of Graphs
摘要：
我们调查的参数化复杂性的概括和变化的支配集问题的类图无处密集。特别是，我们证明了距离d的支配集问题，也被称为（k，d）-中心问题，是固定参数听话的任何类，无处密集和封闭的诱导子图。这推广了已知的结果支配集问题的H-未成年人自由类，类与局部排除未成年人和类的图的有界扩张。我们的证明的一个关键特征是，它是简单地基于这样一个事实，即这些图类是一致的准宽，并不依赖于结构分解。我们的结果还建立了距离d的支配集问题是FPT类的有界扩展，回答了一个问题Ne{ \v s}et{ziness}il和Ossona de Mendez。
英文摘要：
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{ř}il and Ossona de Mendez.
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