Results 61 to 70 of about 7,194,939 (348)
On the Parameterized Complexity of Approximating Dominating Set
Journal of the ACM, 2019 We study the parameterized complexity of approximating the k-Dominating Set (DomSet) problem where an integer k and a graph G on n vertices are given as input, and the goal is to find a dominating set of size at most F(k) ⋅ k whenever the graph G has a ...
S. KarthikC. +2 more
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On the complexity of some hop domination parameters
Electronic Journal of Graph Theory and Applications, 2019 A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
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False alarms in fault-tolerant dominating sets in graphs [PDF]
Opuscula Mathematica, 2012 We develop the problem of fault-tolerant dominating sets (liar's dominating sets) in graphs. Namely, we consider a new kind of fault - a false alarm.
Mateusz Nikodem
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Twin-width III: Max Independent Set, Min Dominating Set, and Coloring
International Colloquium on Automata, Languages and ProgrammingWe recently introduced the notion of twin-width, a novel graph invariant, and showed that first-order model checking can be solved in time f ( d, k ) n for n -vertex graphs given with a witness that the twin-width is at most d , called d -contraction ...
Édouard Bonnet +4 more
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Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems
Mathematics, 2019 The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks.
Ruizhi Li +5 more
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A Fast Local Search Algorithm for Minimum Weight Dominating Set Problem on Massive Graphs
International Joint Conference on Artificial Intelligence, 2018 The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively.
Yiyuan Wang +3 more
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Dominating Vertex Covers: The Vertex-Edge Domination Problem
Discussiones Mathematicae Graph Theory, 2021 The vertex-edge domination number of a graph, γve(G), is defined to be the cardinality of a smallest set D such that there exists a vertex cover C of G such that each vertex in C is dominated by a vertex in D.
Klostermeyer William F. +2 more
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On the independent dominating set polytope
European Journal of Combinatorics, 2006 AbstractIn this paper, we consider the independent dominating set polytope. We give a complete linear description of that polytope when the graph is reduced to a cycle. This description uses a general class of valid inequalities introduced in [T.M. Contenza, Some results on the dominating set polytope, Ph.D. Dissertation, University of Kentucky, 2000].
Mahjoub, A.R., Mailfert, Jean
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Parity of an odd dominating set
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2022 For a simple graph $G$ with vertex set $V(G)=\{v_1,...,v_n\}$, we define the closed neighborhood set of a vertex $u$ as \\$N[u]=\{v \in V(G) \; | \; v \; \text{is adjacent to} \; u \; \text{or} \; v=u \}$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$.
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Eternal Domination: Criticality and Reachability
Discussiones Mathematicae Graph Theory, 2017 We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached.
Klostermeyer William F. +1 more
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