Equitable colorings of planar graphs with maximum degree at least nine

In [Y. Zhang, H.P. Yap, Equitable colorings of planar graphs, J. Combin. Math. Conbin. Comput. 27 (1998) 97–105], Zhang and Yap essentially proved that each planar graph with maximum degree ΔΔ at least 13 has an equitable ΔΔ-coloring. In this paper, we proved that each planar graph in various classes has an equitable ΔΔ-coloring, especially planar graphs with maximum degree 9, 10, 11, and 12. Consequently, each planar graph with maximum degree ΔΔ at least 9 has an equitable ΔΔ-coloring.