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Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function (Extended Abstract) [PDF]
International Joint Conference on Artificial Intelligence, 2017 The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications.
Yiyuan Wang, Shaowei Cai, Minghao Yin
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Locating-dominating sets in hypergraphs [PDF]
Periodica Mathematica Hungarica, 2016 A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the location-domination number of hypergraphs in general and exact values with specified conditions are investigated.
Muhammad Salman +3 more
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Minimal graphs with disjoint dominating and paired-dominating sets
Discussiones Mathematicae Graph Theory, 2021 A subset $D\subseteq V_G$ is a dominating set of $G$ if every vertex in $V_G-D$ has a~neighbor in $D$, while $D$ is a paired-dominating set of $G$ if $D$ is a~dominating set and the subgraph induced by $D$ contains a perfect matching. A graph $G$ is a $D\!P\!D\!P$-graph if it has a pair $(D,P)$ of disjoint sets of vertices of $G$ such that $D$ is a ...
Michael A. Henning, Jerzy Topp
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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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Independent sets with domination constraints [PDF]
Discrete Applied Mathematics, 1998 AbstractA ρ-independent set S in a graph is parameterized by a set ρ of non-negative integers that constrains how the independent set S can dominate the remaining vertices (∀v∉S:|N(v)∩S|∈ρ.) For all values of ρ, we classify as either NP-complete or polynomial-time solvable the problems of deciding if a given graph has a ρ-independent set. We complement
Magnús M. Halldórsson +3 more
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Dominating sets in plane triangulations
Discrete Mathematics, 2010 In 1996, Matheson and Tarjan conjectured that any n-vertex triangulation with n sufficiently large has a dominating set of size at most n/4. We prove this for graphs of maximum degree 6.
Erika L. C. King, Michael J. Pelsmajer
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Lossy Kernels for Connected Dominating Set on Sparse Graphs [PDF]
Symposium on Theoretical Aspects of Computer Science, 2017 Given a graph $G$ and $k\in{\mathbb N}$, the Dominating Set problem asks for a subset $D$ of $k$ vertices such that every vertex in $G$ is either in $D$ or has a neighbor in $D$.
E. Eiben +3 more
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Efficient and Perfect domination on circular-arc graphs [PDF]
, 2015 Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$.
Lin, Min Chih +2 more
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On graphs with disjoint dominating and 2-dominating sets [PDF]
Discussiones Mathematicae Graph Theory, 2013 A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair.
Michael A. Henning, Douglas F. Rall
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Domination, Eternal Domination, and Clique Covering
Discussiones Mathematicae Graph Theory, 2015 Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-
Klostermeyer William F., Mynhardt C.M.
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