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The algorithmic complexity of the minus clique-transversal problem. (English) Zbl 1125.05076
A minus clique-transversal function, MCTF for short, of a graph $$G=(V,E)$$ is a function $$f:V\rightarrow \{-1,0,1\}$$ such that $$\sum_{u\in V(C)}f(u)\geq 1$$ for every clique $$C$$ in $$G$$. The weight of an MCTF $$f$$ is $$\sum_{v\in V}f(v)$$. The minus clique-transversal number of a graph $$G$$ equals the minimum weight of an MCTF of $$G$$. The upper minus clique-transversal number of a graph $$G$$ equals to the maximum weight of a minimal MCTF of $$G$$.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C85 Graph algorithms (graph-theoretic aspects) 68R10 Graph theory (including graph drawing) in computer science
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