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Complexity of Paths, Trails and Circuits in Arc-Colored Digraphs

Gourvès, Laurent; Lyra, Adria; Martinhon, Carlos A.; Monnot, Jérôme (2010), Complexity of Paths, Trails and Circuits in Arc-Colored Digraphs, Theory and Applications of Models of Computation 7th Annual Conference, TAMC 2010, Prague, Czech Republic, June 7-11, 2010. Proceedings, Springer-Verlag : Berlin, p. 222-233. http://dx.doi.org/10.1007/978-3-642-13562-0_21

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Type
Communication / Conférence
Date
2010
Conference title
7th Annual Conference Theory and Applications of Models of Computation (TAMC)
Conference date
2010-06
Conference city
Prague
Conference country
République tchèque
Book title
Theory and Applications of Models of Computation 7th Annual Conference, TAMC 2010, Prague, Czech Republic, June 7-11, 2010. Proceedings
Publisher
Springer-Verlag
Series title
Lecture Notes in Computer Science
Series number
6108/2010
Published in
Berlin
ISBN
978-3-642-13561-3
Pages
222-233
Publication identifier
http://dx.doi.org/10.1007/978-3-642-13562-0_21
Metadata
Show full item record
Author(s)
Gourvès, Laurent
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lyra, Adria

Martinhon, Carlos A.

Monnot, Jérôme cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
We deal with different algorithmic questions regarding properly arc-colored s-t paths, trails and circuits in arc-colored digraphs. Given an arc-colored digraph D c with c ≥ 2 colors, we show that the problem of maximizing the number of arc disjoint properly arc-colored s-t trails can be solved in polynomial time. Surprisingly, we prove that the determination of one properly arc-colored s-t path is NP-complete even for planar digraphs containing no properly arc-colored circuits and c = Ω(n), where n denotes the number of vertices in D c . 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 x (resp., properly arc-colored Hamiltonian s-t path) is NP-complete, even if c = 2. As a consequence, we solve a weak version of an open problem posed in Gutin et. al. [17].
Subjects / Keywords
NP-completeness; Polynomial algorithms; arc-colored tournaments; Hamiltonian directed path; Properly arc-colored paths/trails and circuits; Arc-colored digraphs

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