关于完全3部图的色唯一性

On the chromaticity of complete tripartite graphs

文章设P(G,λ)是图G的色多项式,若对于任意与图G的色多项式相等(P(G,λ)=P(H,λ))的图H都与图G同构(G≌H),则称图G是色唯一图;通过比较3部图的4色类的划分数证明,如果4≤v+2≤k≤2v,n>(k-1)2/4,则完全3部图K(n,n+v,n+k)是色唯一图。

Let P（G,λ） is the chromatic polynomial of a graph G,and the graph G is chromatically unique if for any graph H,P（H,λ）=P（G,λ） implies H≌G.In this paper,by comparing the numbers of partitions into 4-color classes of the tripartite graphs,it is proved that K（n,n＋v,n＋k） is chromatically unique for 4≤v＋2≤k≤2v and n（k-1）2/4.