A plane graph G is entirely k-colorable if \(V(G)\cup E(G) \cup F(G)\) can be colored with k colors such that any two adjacent or incident elements receive different colors. In 2011, Wang and Zhu conjectured that every plane graph G with maximum degree \(\Delta \ge 3\) and \(G\ne K_4\) is entirely \((\Delta +3)\)-colorable. It is known that the conjecture holds for the case \(\Delta \ge 8\). The condition \(\Delta \ge 8\) is improved to \(\Delta \ge 7\) in this paper.

中文翻译：

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$$ \ Delta = 7 $$Δ= 7的平面图完全是10色的

如果\（V（G）\ cup E（G）\ cup F（G）\）可以用k种颜色着色，则任何两个相邻或入射元素接收不同的颜色，则平面图G完全是k色的。在2011年，Wang和诸推测每个平面图形ģ最大度\（\德尔塔\ GE 3 \）和\（G \ NE K_4 \）是完全\（（\德尔塔3）\） -colorable。众所周知，猜想对于情况\（\ Delta \ ge 8 \）成立。本文将条件\（\ Delta \ ge 8 \）改进为\（\ Delta \ ge 7 \）。