Equitable coloring of planar graphs with maximum degree at least eight

The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree $\mathrm{\Delta }\ge 3$ that is not the complete graph $K_{\mathrm{\Delta }+1}$ or the complete bipartite graph $K_{\mathrm{\Delta },\mathrm{\Delta }}$ admits an equitable coloring with $\mathrm{\Delta }$ colors. For planar graphs, the conjecture has been confirmed for $\mathrm{\Delta }\ge 13$ by Yap and Zhang and for $9\le \mathrm{\Delta }\le 12$ by Nakprasit. In this paper, we present a proof that confirms the conjecture for graphs embeddable into a surface with non-negative Euler characteristic with maximum degree $\mathrm{\Delta }\ge 9$ and for planar graphs with maximum degree $\mathrm{\Delta }\ge 8$.