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 such that every vertex in the graph is dominated by at least k vertices in this set. The present paper studies the k-tuple domination problem in graphs from an algorithmic point of view. In particular, we give a linear-time algorithm for the 2-tuple domination problem in trees by employing a labeling method.
"ALGORITHMIC ASPECT OF k-TUPLE DOMINATION IN GRAPHS." Taiwanese J. Math. 6 (3) 415 - 420, 2002. https://doi.org/10.11650/twjm/1500558307