Results 11 to 20 of about 7,194,939 (348)
The complexity of dominating set reconfiguration [PDF]
Theoretical Computer Science, 2015 Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each ...
A Suzuki +11 more
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Distributed Dominating Sets on Grids [PDF]
2013 American Control Conference, 2013 This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids.
Fata, Elaheh +2 more
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Operations Research Letters, 2004 In this paper we study cooperative cost games arising from domination problems on graphs.We introduce three games to model the cost allocation problem and we derive a necessary and su cient condition for the balancedness of all three games.Furthermore we
Velzen, S. van
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Dominating sets in perfect graphs
Discrete Mathematics, 1990 AbstractIn this paper, we review the complexity of the minimum cardinality dominating set problem and some of its variations on several families of perfect graphs. We describe the techniques which are used to attain these complexity results, with emphasis on the dynamic programming approach to the design of algorithms.
Derek G. Corneil, Lorna Stewart
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On the dominating set polytope
European Journal of Combinatorics, 2007 AbstractIn this paper, we study the dominating set polytope in the class of graphs that decompose by one-node cutsets where the pieces are cycles. We describe some classes of facets and procedures to construct facets of the polytope in that class of graphs, and establish some structural properties.
Mustapha Bouchakour +3 more
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Dominating sets and Domination polynomials of Cycles
, 2009 13 pages.
Saeid Alikhani, Yee-Hock Peng
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Reconfiguration of Dominating Sets [PDF]
Journal of Combinatorial Optimization, 2014 12 pages, 4 ...
Amer E. Mouawad +2 more
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Dominating Sets in Planar Graphs
European Journal of Combinatorics, 1996 AbstractMotivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallestεsuch that, fornsufficiently large, everyn-vertex planar graph contains a dominating set of size at mostεn.We prove that 1 ...
Lesley R. Matheson, Robert E. Tarjan
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New Algorithms for Mixed Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.
Louis Dublois +2 more
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Disjoint dominating and 2-dominating sets in graphs [PDF]
Discrete Optimization, 2020 A graph $G$ is a $D\!D_2$-graph if it has a pair $(D,D_2)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_2$ is a 2-dominating set of $G$. We provide several characterizations and hardness results concerning $D\!D_2$-graphs.
Jerzy Topp +2 more
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