# Solving the minimum labeling global cut problem by mathematical programming

Let G = (V, E, L) be an edge-labeled graph such that V is the set of vertices, E is the set of edges, L is the set of labels (colors) and each edge e ∈ E has a label l(e) associated; The goal of the minimum labeling global cut problem (MLGCP) is to find a subset L ⊆ L of labels such that G = (V, E , LŁ ) is not connected and |L| is minimized. This work proposes three new mathematical formulations for the MLGCP as well as branch-and-cut algorithms to solve them. The computational experiments showed that the proposed methods are able to solve small to average sized instances in a reasonable amount of time.

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