The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min\(\{k,d(v)\}\) colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.

中文翻译：

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平面图的弱动态着色

k -图G的弱动态数是我们为G的顶点着色所需的最小颜色数，使得度数d ( v ) 的每个顶点v至少看到min \(\{k,d (v)\}\)其邻域的颜色。我们使用可约配置和图的列表着色来证明所有平面图都具有最多 6 个 3 弱动态数。