Results 61 to 70 of about 7,293,468 (349)
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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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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Some results on domination in annihilating-ideal graphs of commutative rings [PDF]
Journal of Hyperstructures. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are ...
Reza Taheri
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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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Super Dominating Sets in Graphs [PDF]
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015 7 pages, 4 ...
Y. B. Venkatakrishnan +3 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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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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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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Dominating and unbounded free sets [PDF]
Journal of Symbolic Logic, 1999 AbstractWe prove that every analytic set in ωω × ωω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set. and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set ...
Sławomir Solecki +2 more
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