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Let G = (V, E, L) be an edge-labeled graph such that V is the set ofvertices, E is the set of edges, L is the set of labels (colors) and each edgee \in E has a label l(e) associated; The goal of the minimum labeling globalcut problem (MLGCP) is to find a subset L \subseteq L of labels such that G =(V, E , L\L ) is not connected and |L| is minimized. This work proposes threenew mathematical formulations for the MLGCP as well as branch-and-cutalgorithms to solve them. The computational experiments showed that theproposed methods are able to solve small to average sized instances in areasonable amount of time.

Solving the minimum labeling global cut problem by mathematical programming