Preprint
Sep 2026
Total-coloring of planar graphs with maximum degree 6 and without prescribed 4-cycles
The Total Coloring Conjecture (TCC) is a challenging unsolved problem posed by Behzad and Vizing independently, which states that every simple graph $G$ admits a ($\Delta(G)$ +2)-total-coloring, where $\Delta(G)$ denotes the maximum degree of $G$. This conjecture has been confirmed for graphs with $\Delta(G)\leq 5$. Ho...
En-Qiang Zhu, Yang-Yang Zhou, Jin Xu
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