# (Total) Vector domination for graphs with bounded branchwidth

Toshimasa Ishii, Hirotaka Ono, Yushi Uno

2 被引用数 (Scopus)

## 抄録

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⊆V such that every vertex v in V\S (resp., in V) has at least d(v) 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.

本文言語 英語 80-89 10 Discrete Applied Mathematics 207 https://doi.org/10.1016/j.dam.2016.03.002 出版済み - 7月 10 2016

• 離散数学と組合せ数学
• 応用数学

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