Strong oriented chromatic number of planar graphs without cycles of specific lengths

A strong oriented k-coloring of an oriented graph G is a homomorphism φ from G to H having k vertices labelled by the k elements of an abelian additive group M , such that for any pairs of arcs −→ uv and −→ zt of G, we have φ(v)−φ(u) 6= −(φ(t)−φ(z)). The strong oriented chromatic number χs(G) is the smallest k such that G admits a strong oriented k-coloring. In this paper, we consider the following problem: Let i ≥ 4 be an integer. Let G be an oriented planar graph without cycles of lengths 4 to i. What is the strong oriented chromatic number of G?