NDLI: On Paths and Trails in Edge-Colored Graphs and

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On Paths and Trails in Edge-Colored Graphs and

Content Provider	Semantic Scholar
Author	Lyra, Adria
Copyright Year	2009
Abstract	We deal with different algorithmic questions regarding properly edge-colored s-t paths/trails in edge-colored graphs and digraphs. Given a c-edge-colored graph G with no properly edge-colored closed trails, we present a polynomial time procedure for the determination of properly edge-colored s-t trails visiting all vertices of G a predefined number of times. As an immediate consequence, we polynomially solve the Hamiltonian path (resp., Eulerian trail) problem for this particular class of graphs. In addition, we prove that to check whether G contains 2 properly edge-colored s-t paths/trails with length at most L > 0 is NP-complete in the strong sense. Besides, we also show that if G is a general c-edge-colored graph, to find 2 monochromatic vertex disjoint s-t paths with different colors is NP-complete. Regarding c-edge-colored digraphs, we show that the determination of a directed properly edge-colored s-t path is NP-complete in digraphs with c = Ω(n) colors. If the digraph is a c-edge-colored tournament, we show that deciding whether it contains a properly edge-colored circuit passing through a given vertex v (resp., directed st Hamiltonian path) is NP-complete. As a consequence, we solve a weak version of an open problem posed in [30]. In addition, we show that several problems are polynomial if we deal with directed properly edge-colored s-t trails instead of directed properly edge-colored s-t paths.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www2.ic.uff.br/PosGraduacao/Teses/429.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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