Margot, F.Prodon, A.Liebling, Th. M.2006-02-132006-02-132006-02-131988https://infoscience.epfl.ch/handle/20.500.14299/222550The problem of finding p(and even 2) node disjoint paths on a digraph, connecting p pair of terminals is NP-complete. For directed k-trees however, the problem is polynomial. In this paper, we give a linear algorithm for the corresponding optimisation problem on 2-trees and for the case p=2, we characterize te convex hull of the corresponding edge incidence vectors. The optimization algorithm ramains linear and independent of p for k > or equal 3 if the terminals are distincttext::report