Abstract
We describe an exact method to generate the nondominated set of the minimum spanning tree problem with at least two criteria. It is a separation and construction based method whose branching process is done with respect to edges belonging to at least two cycles of a given graph, inducing a step of constructing linear constraints that progressively break cycles while respecting the connectivity of the resulting graph. This has the effect of partitioning the initial graph into subgraphs, each of which corresponds to a discrete multi-objective linear program allowing to find the nondominated set of spanning trees. Randomly generated instances with more than two criteria are provided that show the efficiency of the method.
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