Note on Alternating Directed Cycles (1998) [2 citations — 2 self]
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by Gregory Gutin, Benjamin Sudakov, Anders Yeo
Discrete Math
ftp://ftp.brunel.ac.uk/maths/pub/altdi3.ps
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Abstract:
The problem of the existence of an alternating simple dicycle in a 2-arc-coloured digraph is considered. This is a generalization of the alternating cycle problem in 2-edgecoloured graphs (proved to be polynomial time solvable) and the even dicycle problem (the complexity is not known yet). We prove that the alternating dicycle problem is NP-complete. Let f(n) (g(n), resp.) be the minimum integer such that if every monochromatic indegree and outdegree in a strongly connected 2-arc-coloured digraph (any 2-arccoloured digraph, resp.) D is at least f(n) (g(n), resp.), then D has an alternating simple dicycle. We show that f(n) = \Theta(log n) and g(n) = \Theta(log n).
Citations
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| 10 | Cycles of length 0 modulo k in directed graphs – Alon, Linial - 1989 |
| 9 | The even cycle problem for planar digraphs – Thomassen - 1993 |
| 8 | Alternating cycles and paths in edge-coloured multigraphs: a survey. Discrete Math – Bang-Jensen, Gutin - 1997 |
