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On the complexity of path problems in properly colored directed graphs

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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.

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Authors and Affiliations

  1. Department of Statistics, Probability and Applied Statistics, University of Rome “La Sapienza”, P.le Aldo Moro 5, Rome, Italy

    Donatella Granata

  2. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611, USA

    Behnam Behdani

  3. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611, USA

    Panos M. Pardalos

Authors
  1. Donatella Granata
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  2. Behnam Behdani
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  3. Panos M. Pardalos
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Corresponding author

Correspondence to Donatella Granata.

Additional information

This research is partially supported by DTRA and Air Force grants.

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Granata, D., Behdani, B. & Pardalos, P.M. On the complexity of path problems in properly colored directed graphs. J Comb Optim 24, 459–467 (2012). https://doi.org/10.1007/s10878-011-9401-7

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  • DOI: https://doi.org/10.1007/s10878-011-9401-7

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