An orientation of an undirected graph G is a directed graph D on V(G) with exactly one of directed edges (u, v) and (v, u) for each pair of vertices u and v adjacent in G. For integer k ≥ 3, we say a directed graph D is k-cyclic if every edge of D belongs to a directed cycle in D of length at most k. We consider the problem of deciding if a given graph has a k-cyclic orientation. We show that this problem is NP-complete for every fixed k ≥ 3 for general graphs and for every fixed k ≥ 4 for planar graphs. We give a polynomial time algorithm for planar graphs with k ≥ 3, which constructs a 3-cyclic orientation when the answer is affirmative. © 2010 Springer-Verlag.
CITATION STYLE
Kobayashi, Y., Miyamoto, Y., & Tamaki, H. (2010). k-cyclic orientations of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6507 LNCS, pp. 73–84). https://doi.org/10.1007/978-3-642-17514-5_7
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