Arborescence polytopes for series-parallel graphs

This paper considers some polytopes associated with arborescences in a series-parallel graph. The main result is a complete characterization by linear inequalities of the convex hull of incidence vectors of rooted arborescences. As a consequence, a complete description of the Steiner arborescence polytope is obtained. A new proof of Prodon et al’s characterization of the dominant of the Steiner arborescence polytope is also suggested. All the present results are valid only if the underlying graph is series-parallel.