# On the acyclic subgraph polytope

@article{Grtschel1985OnTA, title={On the acyclic subgraph polytope}, author={Martin Gr{\"o}tschel and Michael J{\"u}nger and Gerhard Reinelt}, journal={Mathematical Programming}, year={1985}, volume={33}, pages={28-42} }

The acyclic subgraph problem can be formulated as follows. Given a digraph with arc weights, find a set of arcs containing no directed cycle and having maximum total weight. We investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope. We also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time. This implies that the acyclic subgraph problem can be solved…

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