Hardness results and approximation algorithms for (weighted) paired-domination in graphs
نویسندگان
چکیده
منابع مشابه
Paired-Domination Game Played in Graphs
In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...
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The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or v has a neighbor in S, or (2) v has a neighbor w such that w and all of its neighbors except v are power dominated. We show a hardness of approximation threshold o...
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A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...
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We introduce a hierarchy of problems between the Dominating Set problem and the Power Dominating Set (PDS) problem called the l-round power dominating set (l-round PDS, for short) problem. For l = 1, this is the Dominating Set problem, and for l ≥ n − 1, this is the PDS problem; here n denotes the number of nodes in the input graph. In PDS the goal is to find a minimum size set of nodes S that ...
متن کاملPaired-domination in inflated graphs
The inflation GI of a graph G with n(G) vertices and m(G) edges is obtained from G by replacing every vertex of degree d of G by a clique Kd. A set S of vertices in a graph G is a paired dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired domination number γp(G) is the minimum cardinality of a paired d...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.08.004