On Complexities of Minus Domination
Abstract
A function f: V \rightarrow \{-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 \in V. The minus-domination number \gamma^{-}(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 minus-dominating 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. 79,1 5%
Keywords
Cite
@article{arxiv.1307.6663,
title = {On Complexities of Minus Domination},
author = {Luérbio Faria and Wing-Kai Hon and Ton Kloks and Hsiang-Hsuan Liu and Tao-Ming Wang and Yue-Li Wang},
journal= {arXiv preprint arXiv:1307.6663},
year = {2013}
}