On negative cycles in mixed graphs

  • Authors:

  • Esther M Arkin;Christos H Papadimitriou

  • Affiliations:

  • Department of Operations Research, Stanford University, Stanford, CA 94305, USA;Department of Operations Research, Stanford University, Stanford, CA 94305, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1985

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Abstract

We show that, for mixed graphs, i.e., graphs having both directed and undirected edges, with a length function defined on the edges, the problems of detecting negative cycles and of finding the shortest path in the absence of negative cycles are NP-complete.