On Integrality, Stability and Composition of Dicycle Packings and Covers

  title={On Integrality, Stability and Composition of Dicycle Packings and Covers},
  author={Zeev Nutov and Michal Penn},
  journal={Journal of Combinatorial Optimization},
  • Zeev Nutov, M. Penn
  • Published 1 June 2000
  • Mathematics
  • Journal of Combinatorial Optimization
Given a digraph D, the minimum integral dicycle cover problem (known also as the minimum feedback arc set problem) is to find a minimum set of arcs that intersects every dicycle; the maximum integral dicycle packing problem is to find a maximum set of pairwise arc disjoint dicycles. These two problems are NP-complete.Assume D has a 2-vertex cut. We show how to derive a minimum dicycle cover (a maximum dicycle packing) for D, by composing certain covers (packings) of the corresponding pieces… 



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