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Complexity of trails, paths and circuits in arc-colored digraphs

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Date
2013
Dewey
Recherche opérationnelle
Sujet
Properly arc-colored paths/trails and circuits; Arc-colored digraphs; Hamiltonian directed path; Arc-colored tournaments; Polynomial algorithms; NP-completeness
Journal issue
Discrete Applied Mathematics
Volume
161
Number
6
Publication date
2013
Article pages
819-828
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.dam.2012.10.025
URI
https://basepub.dauphine.fr/handle/123456789/11469
Collections
  • LAMSADE : Publications
Metadata
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Author
Gourvès, Laurent
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lyra, Adria
status unknown
Martinhon, Carlos A.
status unknown
Monnot, Jérôme
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We deal with different algorithmic questions regarding properly arc-colored s–ts–t trails, paths and circuits in arc-colored digraphs. Given an arc-colored digraph DcDc with c≥2c≥2 colors, we show that the problem of determining the maximum number of arc disjoint properly arc-colored s–ts–t trails can be solved in polynomial time. Surprisingly, we prove that the determination of a properly arc-colored s–ts–t path is NP-complete even for planar digraphs containing no properly arc-colored circuits and c=Ω(n)c=Ω(n), where nn denotes the number of vertices in DcDc. If the digraph is an arc-colored tournament, we show that deciding whether it contains a properly arc-colored circuit passing through a given vertex xx (resp., properly arc-colored Hamiltonian s–ts–t path) is NP-complete for c≥2c≥2. As a consequence, we solve a weak version of an open problem posed in Gutin et al. (1998) [23], whose objective is to determine whether a 22-arc-colored tournament contains a properly arc-colored circuit.

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