On the complexity of path problems in properly colored directed graphs

  • Authors:

  • Donatella Granata;Behnam Behdani;Panos M. Pardalos

  • Affiliations:

  • Department of Statistics, Probability and Applied Statistics, University of Rome "La Sapienza", Rome, Italy;Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611;Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

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Abstract

We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into $\mathcal{X}(G)$ stable subsets, where $\mathcal{X}(G)$ denotes the chromatic number of G. We show that to find a simple path that meets all the colors in a properly colored directed graph is NP-complete, and so are the problems of finding a shortest and longest of such paths between two specific nodes.