  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%

Discrete Mathematics;Combinatorics