Paper Info
Title
Complexity of paths, trails and circuits in arc-colored digraphs
Abstract
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 Dc 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 Dc 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].
Year
DOI
Venue
2010
10.1007/978-3-642-13562-0_21
TAMC
Keywords
Field
DocType
arc-colored s-t,open problem,arc-colored tournament,arc disjoint,planar digraph,arc-colored digraph,arc-colored s-t path,arc-colored circuit,hamiltonian s-t path,arc-colored digraph dc,np completeness,polynomial time
Discrete mathematics,Combinatorics,Tournament,Open problem,Arc (geometry),Disjoint sets,Vertex (geometry),Hamiltonian (quantum mechanics),Time complexity,Digraph,Mathematics
Conference
Volume
ISSN
ISBN
6108
0302-9743
3-642-13561-7
Citations 
PageRank 
References 
3
0.43
17
Authors
4
Name
Order
Citations
PageRank
Laurent Gourvès124130.97
Adria Lyra2333.02
Carlos Martinhon3251.78
Jérôme Monnot451255.74