Complexity of the oriented coloring in planar, cubic oriented graphs
نویسندگان
چکیده
An oriented k-coloring of an oriented graph ~ G = (V, ~ E) is a partition of V into k subsets such that there are no two adjacent vertices belonging to the same subset and all the arcs between a pair of subsets have the same orientation. The decision problem k-oriented chromatic number (ocnk) consists of an oriented graph ~ G and an integer k > 0, plus the question if there exists an oriented kcoloring of ~ G. Many papers have presented NP-completeness proofs for ocnk (e.g., see [BJHM88, CFGK13, CD06, GH10, KM04]). We noticed that it was not known the complexity status of ocnk when the input graph ~ G satisfies that the underlying graph G is cubic. In this work we prove that ocn4 remains NP-complete even when restricted to a connected, planar and cubic oriented graph ~ G.
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