平环图着色的性质

Properties of coloring the annular region

利用色多项式的零点问题的性质研究了平面图的着色问题,主要研究平环中具有n个区域以及剖分后得到的图进行着色性质,也就是使得相邻两个区域着不同色.首先,研究了带有n个区域平环图Gn的最小涂色数目,并且该图进行广义三角剖分,研究了广义三角剖分后图的涂色数目的性质;其次,讨论了两个这样图组合在一起,就是两个具有一条公共边Gt和Gs组成区域图的性质,讨论这些图及其广义三角剖分后图的涂色性质.进而证明这些图在剖分前后的着色的性质是不变的.

The coloring problem for graph is studied by using the nature of zero point problem of the chromatic polynomial.The coloring properties of annulus region with n regions,when the adjacent areas have different colors,is mainly discussed.Firstly,the minimum coloring number of n-region graph is discussed and expanded to generalized subdivision.Secondly,the two graphs(including generalized subdivision)with a common edge is studies for the coloring properties.It is proven that the coloring properties of these graphs are invariable before and after the subdivision.