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Abstract: An oriented k-coloring of an oriented graph 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 (ocn k ) consists of an oriented graph and an integer , plus the question if there exists an oriented k-coloring of . We present a proof that ocn 4 is NP-complete for an acyclic oriented graph such that the underlying graph has maximum degree 3 and it is at the same time connected, planar and bipartite. Our result is optimum, since ocn 3 is in P, and ocn k is also in P when the underlying graph has maximum degree 2. [Copyright &y& Elsevier]