完全3部图K(n-k,n-3,n)色唯一性的证明（英文）  

Proof of chromaticity of the complete tripartite graphs K(n-k,n-3,n)

作　　者：徐利民[1] 杨志林[2] XU Limin;YANG Zhilin(Department of Humanities Education,Huainan Vocational and Technical College,Huainan 232001,China;School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]淮南职业技术学院人文教育系,安徽淮南232001 [2]合肥工业大学数学学院,安徽合肥230009

出　　处：《中国科学技术大学学报》2019年第5期377-381,共5页JUSTC

基　　金：Supported by the Natural Science Research Project of Higher Education of Anhui(KJ2015A404)

摘　　要：设P(G,λ)是图G的色多项式,如果任意与图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.这里,通过比较图的三角形子图和无弦四边形的个数,完全解决了一类完全三部图K(n-k,n-3,n)的色唯一性问题,证明了,若n≥k+2≥5,则完全三部图K(n-k,n-3,n)是色唯一图.Let P(G,λ)be the chromatic polynomial of a graph G.A graph Gis chromatically unique if for any graph H,P(H,λ)=P(G,λ)implies G≌H.Here,by comparing the number of the triangular subgraphs and the number of the quadrangular subgraphs without chords,the chromatic uniqueness problem of the complete tripartite graphs K(n-k,n-3,n)was completely solved.It was proved that K(n-k,n-3,n)is chromatically unique if n≥k+2≥5.

关 键 词：完全三部图 色唯一性 三角形子图 无弦四边形子图 

分 类 号：O157.5[理学—数学]