设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:2...设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:259-285]中提出的猜想(若n≥k+2,则完全三部图K(n-k,n,n)是色唯一图);推广了文献[Liu Ru-yin,Zhao Hai-xing,Ye Cheng-fu.A complete solution to a conjecture on chromatic unique of complete tripartite graphs.Discrete Mathematics,2004,289:175-179]中的结果(若n≥k+2≥4,则K(n-k,n,n)是色唯一图;若n≥2k≥4,则K(n-k,n-1,n)是色唯一图);证明了若n≥k+2≥4,则K(n-k,n,…,n)是色唯一图,若n≥k+2≥4,则K(n-k,n-1,n,…,n)是色唯一图.展开更多
In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition o...In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.展开更多
文摘设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:259-285]中提出的猜想(若n≥k+2,则完全三部图K(n-k,n,n)是色唯一图);推广了文献[Liu Ru-yin,Zhao Hai-xing,Ye Cheng-fu.A complete solution to a conjecture on chromatic unique of complete tripartite graphs.Discrete Mathematics,2004,289:175-179]中的结果(若n≥k+2≥4,则K(n-k,n,n)是色唯一图;若n≥2k≥4,则K(n-k,n-1,n)是色唯一图);证明了若n≥k+2≥4,则K(n-k,n,…,n)是色唯一图,若n≥k+2≥4,则K(n-k,n-1,n,…,n)是色唯一图.
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 1 1 0 )
文摘In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.
