完全t部图K(n_1,n_2…n_t)的色唯一性

On the Chromaticity of Complete t -partite GraphsK(n1,n2…,ni)

本文使用比较两个色等价图的色划分数的方法,得出了完全t部图的色等价图类仍为完全t部图的一般形式数值条件,进一步得出了K(n_1,n_2,n_3)和K(n_1,n_2,n_3,n_4)为色唯一图的一般形式数值条件。

With Comparing the numbers of partions into r color classes of two chromatically equivalent graphs, a general numerical condition is established to guarante that the equivalent graphs of complete t-partite graphs K(n1,n2,...,nt) are still complete t-partite graphs. Furthermore, two general numerical conditions are obtained, under which K(n1,n2,nt) and K(n1,n2,n3,n4) are chromatically unique.