Acircuitic directed star arboricity of planar graphs with large girth

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G is the minimum number of edge-disjoint directed star forests whose union covers all edges of G and such that the union of two such forests is acircuitic. We show that graphs with maximum average degree less than 7 3 (resp. 133 41 ) have acircuitic directed star arboricity at most ∆ (resp. ∆+1); this implies that planar graphs of girth at least 14 (resp. 6) have acircuitic directed star arboricity at most ∆ (resp. ∆ + 1).