A plane graph G is edge‐face k‐colorable if its edges and faces can be colored with k colors such that any two adjacent or incident elements receive different colors. It is known that every plane graph G of maximum degree Δ ≥ 8 is edge‐face (Δ + 1)‐colorable. The condition Δ ≥ 8 is improved to Δ ≥ 7 in this paper.

中文翻译：

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最大度Δ≥7的平面图是边缘面（Δ+1）-可着色

如果平面图G的边缘和面可以用k种颜色着色，使得任意两个相邻或入射元素接收不同的颜色，则该平面图G可以是k面。众所周知，最大度数Δ≥8的每个平面图G都是边-面（Δ+1）-可着色的。本文将Δ≥8的条件改进为Δ≥7。