Graph theory with applications to algorithms and computer science
Doubly lexical orderings of matrices
SIAM Journal on Computing
Three partition refinement algorithms
SIAM Journal on Computing
Labeling algorithms for domination problems in sun-free chordal graphs
Discrete Applied Mathematics
Doubly lexical ordering of dense 0–1 matrices
Information Processing Letters
Nordhaus-Gaddum inequalities for domination in graphs
Discrete Mathematics - Special issue on combinatorics
Journal of the ACM (JACM)
Hardness results and approximation algorithms of k-tuple domination in graphs
Information Processing Letters
On Constructing k-Connected k-Dominating Set in Wireless Networks
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
On constructing k-connected k-dominating set in wireless ad hoc and sensor networks
Journal of Parallel and Distributed Computing - 19th International parallel and distributed processing symposium
Toward Broadcast Reliability in Mobile Ad Hoc Networks with Double Coverage
IEEE Transactions on Mobile Computing
On the k-tuple domination of de Bruijn and Kautz digraphs
Information Processing Letters
The upper bound on k-tuple domination numbers of graphs
European Journal of Combinatorics
Approximating the Spanning k-Tree Forest Problem
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
A linear-time algorithm for paired-domination problem in strongly chordal graphs
Information Processing Letters
k-tuple total domination in graphs
Discrete Applied Mathematics
Capacitated domination problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On the k-tuple domination of generalized de Brujin and Kautz digraphs
Information Sciences: an International Journal
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
The multiple domination and limited packing problems in graphs
Information Processing Letters
Strong Transversals in Hypergraphs and Double Total Domination in Graphs
SIAM Journal on Discrete Mathematics
Power domination problem in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Algorithmic aspects of k-tuple total domination in graphs
Information Processing Letters
Complexity of distance paired-domination problem in graphs
Theoretical Computer Science
k-tuple total domination in cross products of graphs
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization
On the approximability and exact algorithms for vector domination and related problems in graphs
Discrete Applied Mathematics
Rainbow domination and related problems on strongly chordal graphs
Discrete Applied Mathematics
Limited Packing and Multiple Domination problems: Polynomial time reductions
Discrete Applied Mathematics
Paired versus double domination in K1,r-free graphs
Journal of Combinatorial Optimization
Hardness results and approximation algorithm for total liar's domination in graphs
Journal of Combinatorial Optimization
| Hi-index | 0.89 |
In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the k-tuple domination problem is to find a minimum sized vertex subset in a graph such that every vertex in the graph is dominated by at least k vertices in this set. The current paper studies k-tuple domination in graphs from an algorithmic point of view. In particular, we give a linear-time algorithm for the k-tuple domination problem in strongly chordal graphs, which is a subclass of chordal graphs and includes trees, block graphs, interval graphs and directed path graphs. We also prove that the k-tuple domination problem is NP-complete for split graphs (a subclass of chordal graphs) and for bipartite graphs.