An oriented coloring of planar graphs with girth at least five

An oriented k -coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k . We prove that every oriented graph with a maximum average degree less than 10 3 and girth at least 5 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to Borodin et al. [O.V. Borodin, A.V. Kostochka, J. Nešetřil, A. Raspaud, É. Sopena, On the maximum average degree and the oriented chromatic number of a graph, Discrete Math. 206 (1999) 77–89].