Journal of Combinatorial Optimization

, Volume 24, Issue 4, pp 459–467 | Cite as

On the complexity of path problems in properly colored directed graphs

  • Donatella GranataEmail author
  • Behnam Behdani
  • Panos M. Pardalos


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.


Graph coloring Complexity Chromatic number Longest path Shortest path 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Donatella Granata
    • 1
    Email author
  • Behnam Behdani
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.Department of Statistics, Probability and Applied StatisticsUniversity of Rome “La Sapienza”RomeItaly
  2. 2.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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