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完全图与完全n部图的完全多部图分解
引用本文:黄庆学.完全图与完全n部图的完全多部图分解[J].高校应用数学学报(英文版),2003,18(3).
作者姓名:黄庆学
作者单位:Huang QingxueDept. of Math.,Zhejiang Univ.,Hangzhou 310027,China.
基金项目:Supported by the National Natural Science Foundation of China( 1 0 2 71 1 1 0 )
摘    要:§ 1 IntroductionLet V(G) and E(G) be the vertex setand the edge setof a graph G,respectively.Fori=1 ,...,p,if V(Gi) V(G) ,E(Gi)∩ E(Gj) = for i≠ j,and∪pi=1 E(Gi) =E(G) ,then wecall{ G1 ,...,GP} a decomposition of G.Leti,j] be the integer interval including i and j.Let Knbe a complete graph with the vertex set1 ,n] .For m disjointsubsets A1 ,...Amof1 ,n] ,let K(A1 ,...,Am) be a complete m-partite graph having partite-sets A1 ,...,Am.If| Ai| =1 ,Ai is called a S-set;otherwi…


COMPLETE MULTIPARTITE DECOMPOSITIONS OF COMPLETE GRAPHS AND COMPLETE n-PARTITE GRAPHS
Huang Qingxue.COMPLETE MULTIPARTITE DECOMPOSITIONS OF COMPLETE GRAPHS AND COMPLETE n-PARTITE GRAPHS[J].Applied Mathematics A Journal of Chinese Universities,2003,18(3).
Authors:Huang Qingxue
Abstract: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.
Keywords:complete n-partite graph  decomposition of graph  complete multipartite decomposition
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