2 research outputs found
{Linear Kernels for -Tupel and Liar's Domination in Bounded Genus Graphs}
A set is called a -tuple dominating set of a graph if for all , where denotes the closed neighborhood of . A set is called a liar's dominating set of a graph if (i) for all and (ii) for every pair of distinct vertices , . Given a graph , the decision versions of -Tuple Domination Problem and the Liar's Domination Problem are to check whether there exists a -tuple dominating set and a liar's dominating set of of a given cardinality, respectively. These two problems are known to be NP-complete \cite{LiaoChang2003, Slater2009}. In this paper, we study the parameterized complexity of these problems. We show that the -Tuple Domination Problem and the Liar's Domination Problem are -hard for general graphs but they admit linear kernels for graphs with bounded genus.Title changed from "Parameterized complexity of k-tuple and liar's domination" to "Linear kernels for k-tuple and liar's domination in bounded genus graphs