### 抜粋

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.

元の言語 | 英語 |
---|---|

ページ（範囲） | 80-89 |

ページ数 | 10 |

ジャーナル | Discrete Applied Mathematics |

巻 | 207 |

DOI | |

出版物ステータス | 出版済み - 7 10 2016 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### これを引用

*Discrete Applied Mathematics*,

*207*, 80-89. https://doi.org/10.1016/j.dam.2016.03.002