On Complexities of Minus Domination

نویسندگان

  • Luérbio Faria
  • Wing-Kai Hon
  • Ton Kloks
  • Hsiang Hsuan Liu
  • Tao-Ming Wang
  • Yue-Li Wang
چکیده

A function f : V → {−1, 0, 1} is a minus-domination function of a graph G = (V,E) if the values over the vertices in each closed neighborhood sum to a positive number. The weight of f is the sum of f(x) over all vertices x ∈ V. The minus-domination number γ(G) is the minimum weight over all minus-domination functions. The size of a minus domination is the number of vertices that are assigned 1. In this paper we show that the minus-domination problem is fixed-parameter tractable for d-degenerate graphs when parameterized by the size of the minusdominating set and by d. The minus-domination problem is polynomial for graphs of bounded rankwidth and for strongly chordal graphs. It is NP-complete for splitgraphs. Unless P = NP there is no fixed-parameter algorithm for minus-domination.

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تاریخ انتشار 2013