The 2 edge-disjoint 3-paths polyhedron

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 = 2 and 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 = 2 and L = 3. We use a reduction of the problem to a size-2 stable
set problem to prove this second property.