We develop a connection between vertex coloring in graphs and star arboricity which allows us to prove that every planar graph has star arboricity at most 5. This settles an open problem raised independently by Algor and Alon and by Ringel. We also show that deciding if a graph has star arboricity 2 is NP-complete, even for 2-degenerate graphs.
Hakimi, S. L., Mitchem, J., & Schmeichel, E. (1996). Star arboricity of graphs. Discrete Mathematics, 149(1–3), 93–98. https://doi.org/10.1016/0012-365X(94)00313-8