Results 1 to 10 of about 50,196 (100)
Reconfiguration of Dominating Sets [PDF]
Journal of Combinatorial Optimization, 2014 12 pages, 4 ...
Suzuki, Akira +2 more
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Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]
, 2019 In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time $O( \cdot \text{polylog}~n)$ per update, where $ $ is the maximum vertex degree in the
Hjuler N. +3 more
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Dominating Sets and Domination Polynomials of Paths [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 Let G = (V, E) be a simple graph. A set S⊆V is a dominating set of G, if every vertex in V\S is adjacent to at least one vertex in S. Let be the family of all dominating sets of a path Pn with cardinality i, and let . In this paper, we construct , and obtain a recursive formula for d(Pn, i).
Saeid Alikhani, Yee-Hock Peng
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Operations Research Letters, 2004 This paper presents several representation theorems for the solubility of three cost allocation problems, which are presented as cooperative games. In each problem, a graph \(G = (V, E)\) is given along with a cost function: given \(S \subseteq V\), \(c(S)\) is the cost of \(k\)-dominating the vertices in \(S\), i.e., building a set \(K \subseteq V ...
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Distributed dominating sets on grids [PDF]
2013 American Control Conference, 2013 10 pages, 9 figures, accepted in ACC ...
Fata, Elaheh +2 more
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, 2022 We consider a minimizing variant of the well-known \emph{No-Three-In-Line Problem}, the \emph{Geometric Dominating Set Problem}: What is the smallest number of points in an $n\times n$~grid such that every grid point lies on a common line with two of the points in the set?
Aichholzer, Oswin +2 more
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On redundant locating-dominating sets
Discrete Applied Mathematics, 2023 A locating-dominating set in a graph G is a subset of vertices representing "detectors" which can locate an "intruder" given that each detector covers its closed neighborhood and can distinguish its own location from its neighbors. We explore a fault-tolerant variant of locating-dominating sets called redundant locating-dominating sets, which can ...
Devin C. Jean, Suk J. Seo
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Weighted Domination of Independent Sets [PDF]
Graphs and Combinatorics, 2019 The {\em independent domination number} $ ^i(G)$ of a graph $G$ is the maximum, over all independent sets $I$, of the minimal number of vertices needed to dominate $I$. It is known \cite{abz} that in chordal graphs $ ^i$ is equal to $ $, the ordinary domination number.
Aharoni, Ron, Gorelik, Irina
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Edge Dominating Sets in Graphs [PDF]
SIAM Journal on Applied Mathematics, 1980 We prove that the edge dominating set problem for graphs is $NP$-complete even when restricted to planar or bipartite graphs of maximum degree 3. We show as a corollary that the minimum maximal matching and the achromatic number problems are $NP$-complete.
Yannakakis, M., Gavril, F.
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