中文摘要：

本文利用平面色多项式的性质研究某些平面图着色的问题,特别是研究了平面图通过广义三角剖分和三角剖分后着色的性质,通过讨论图的色多项式的零点问题,分析对应图的着色,保证相邻的两个区域着不同颜色的最少方法数目,进而给出了平面剖分图的着色方法数目的重要性质.证明了某些图的最小着色数在广义三角剖分和三角剖分下是保持不变的.

英文摘要：

In this paper, it studies the properties of coloring some plane graphs by using the properties of chromatic polynomial of plane graphs. It deals with mainly the properties of coloring some plane graphs after triangulation and generalized division. It studies the smallest number of ways to faces-color the graph with colors so that no two adjacent faces receive the same color, by discussing the zeros of the chromatic polynomial of graphs. And given the important properties of the number of ways to color plane division graphs. It proofs that the smallest number of coloring some plane graphs is not change under triangulation and generalized division.