Classes of bipartite graphs related to chordal graphs
Discrete Applied Mathematics
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
SIAM Journal on Discrete Mathematics
Introduction to algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Information Processing Letters
Hardness results and approximation algorithms of k-tuple domination in graphs
Information Processing Letters
Approximation hardness of dominating set problems in bounded degree graphs
Information and Computation
k-tuple total domination in graphs
Discrete Applied Mathematics
Computing a minimum outer-connected dominating set for the class of chordal graphs
Information Processing Letters
Efficient self-stabilizing algorithms for minimal total k-dominating sets in graphs
Information Processing Letters
| Hi-index | 0.89 |
For a fixed positive integer k, a k-tuple total dominating set of a graph G=(V,E) is a subset TD"k of V such that every vertex in V is adjacent to at least k vertices of TD"k. In minimum k-tuple total dominating set problem (Mink-Tuple Total Dom Set), it is required to find a k-tuple total dominating set of minimum cardinality and Decide Mink-Tuple Total Dom Set is the decision version of Mink-Tuple Total Dom Set problem. In this paper, we show that Decide Mink-Tuple Total Dom Set is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that Mink-Tuple Total Dom Set can be solved in polynomial time. We also propose some hardness results and approximation algorithms for Mink-Tuple Total Dom Set problem.