Complexity of Unique (Optimal) Solutions in Graphs: Vertex Cover and Domination
Résumé
We study the complexity of four decision problems dealing with the uniqueness of a solution in a graph: "Uniqueness of a Vertex Cover with bounded size"(U-VC) and "Uniqueness of an Optimal Vertex Cover"(U-OVC), and for any fixed integer r ≥ 1, "Uniqueness of an r-Dominating Code with bounded size" (U-DCr) and "Uniqueness of an Optimal r-Dominating Code" (U-ODCr). In particular, we give a polynomial reduction from "Unique Satisfiability of a Boolean formula" (U-SAT
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