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Arborescence polytopes for series-parallel graphs. (English) Zbl 0802.05040
A graph is called series-parallel if it does not contain any subgraph homeomorphic to the complete graph on 4 vertices. For a directed graph whose underlying graph is series-parallel, an $$r$$-arborescence is defined as a tree directed away from the root vertex $$r$$. Given a set of terminals, a Steiner arborescence is an $$r$$-arborescence spanning this set. Associated with these arborescences the author defines the convex hulls of incidence vectors and characterizes these polytopes completely by linear inequalities.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C05 Trees 05C99 Graph theory
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