(Total) Vector domination for graphs with bounded branchwidth

作者：Ishii Toshimasa^*; Ono Hirotaka; Uno Yushi

来源：Discrete Applied Mathematics, 2016, 207: 80-89.

DOI：10.1016/j.dam.2016.03.002

• Vector dominating set
• Total vector dominating set
• Multiple dominating set
• FPT
• Bounded branchwidth

Given a graph G = (V, E) of order n and an n-dimensional non-negative vector d = (d(1), d(2),..., d(n)), called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum S subset of V such that every vertex nu in V \ S (resp., in V) has at least d(nu) neighbors in S. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the k-tuple dominating set problem (this k is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respect to k, where k is the size of solution.

• 出版日期2016-7-10