The Vertex k-cut Problem
نویسندگان
چکیده
Given an undirected graph G = (V,E), a vertex k-cut of G is a vertex subset of V the removing of which disconnects the graph in at least k connected components. Given a graph G and an integer k ≥ 2, the vertex k-cut problem consists in finding a vertex k-cut of G of minimum cardinality. We first prove that the problem is NP-hard for any fixed k ≥ 3. We then present a compact formulation, and an extended formulation from which we derive a column generation and a branching scheme. Extensive computational results prove the effectiveness of the proposed methods. keywords: Vertex Cut, Mixed-Integer Programming Models, Branch and Price, Exact Algorithms.
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