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arXiv · 2305.12041

Equitable coloring of planar graphs with maximum degree at least eight

Alexandr Kostochka·Duo Lin·Zimu Xiang
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Abstract

The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree $\Delta\geq 3$ that is not the complete graph $K_{\Delta+1}$ or the complete bipartite graph $K_{\Delta,\Delta}$ admits an equitable coloring with $\Delta$ colors. For planar graphs, the conjecture has been confirmed for $\Delta\geq 13$ by Yap and Zhang and for $9\leq \Delta\leq 12$ 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 $\Delta\geq 9$ and for planar graphs with maximum degree $\Delta\geq 8$.

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Alexandr Kostochka, Duo Lin, Zimu Xiang. 2023-05-19. Equitable coloring of planar graphs with maximum degree at least eight. https://arxiv.org/abs/2305.12041

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