Abstract
Given an undirected graph, we study the problem of finding K edge-disjoint paths, each one containing at most L edges, between a given pair of nodes. We focus on the case of K = 2and L = 3. For this particular case, previous known compact formulations are valid only for the case with non-negative edge costs. We provide the first compact linear description that is also valid for general edge costs. We describe new valid inequalities that are added to a well known extended formulation in a layered graph, to get a full description of the polyhedron for K = 2and L = 3. We use a reduction of the problem to a size-2 stable set problem to prove this second property.
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