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On the acyclic subgraph polytope

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Abstract

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 in polynomial time for weakly acyclic digraphs. This generalizes a result of Lucchesi for planar digraphs.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Memminger Str. 6, D-8900, Augsburg, FR Germany

    Martin Grötschel, Michael Jünger & Gerhard Reinelt

Authors
  1. Martin Grötschel
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  2. Michael Jünger
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  3. Gerhard Reinelt
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Grötschel, M., Jünger, M. & Reinelt, G. On the acyclic subgraph polytope. Mathematical Programming 33, 28–42 (1985). https://doi.org/10.1007/BF01582009

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  • DOI: https://doi.org/10.1007/BF01582009

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