五点八边图的完美T(G)-三元系  

Perfect T(G)-triple System for Each Subgraph G of K_5 with Eight Edges

作　　者：侯英涛[1] 康庆德[2] 张艳丽[3] 

机构地区：[1]保定电力职业技术学院基础教学部,保定071051 [2]河北师范大学数学研究所,石家庄050016 [3]石家庄经济学院华信学院科学技术系,石家庄050091

出　　处：《应用数学学报》2011年第5期830-837,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10971051);河北省自然科学基金(A2010000353)资助项目

摘　　要：设G是K_n的子图.在G的每边外添加一点,将该边扩展为一个3长圈,且所添加的点两两不同,均异于G的诸顶点,这样得到的图形被记为T(G).如果3K_n的边恰好能够分拆成与T(G)同构的一些子图,则称这些子图构成一个n阶的T(G)-三元系.进而,若此分拆的全体内部边又恰构成K_n中全部边的一个分拆,则称这个T(G)-三元系是完美的.对于所有使得完美T(G)-三元系存在的正整数n的集合称为完美T(G)-三元系的存在谱.对于K_4的所有子图及K_5的7边以下子图G,其完美T(G)-三元系的存在性问题已经在一系列文章中被完全解决.本文将对不含孤立点的全部五点八边图G,确定完美T(G)-三元系的存在谱.Let G be a subgraph of Kn. The graph obtained from G by replacing each edge with a 3-cycle whose third vertex is distinct from other vertices in the configuration is called a T（G）-triple. An edge-disjoint decomposition of 3Kn into copies of T（G） is called a T（G）-triple system of order n. If, i：a each copy of T（G） in a T（G）-triple system, one edge is taken from each 3-cycle （chosen so that these edges ：~orm a copy of G） in such a way that the resulting copies of G form an edge-disjoint decomposition of Kn, then the T（G）-triple system is said to be perfect. The set of positive integers n for which a perfect T（G）-triple system exists is called its spectrum. A series of earlier papers determined the spectra for cases where G is any subgraph of K4. Then, in our previous paper, the spectrum of perfect T（G）-triple systems for each graph G with five vertices and i（≤7） edges was determined. In this paper, we will completely solve the spectrum problem of perfect T（G）-triple system for each subgraph G of K5 with eight edges.

关 键 词：T(G) T(G)-三元系 完全T(G)-三元系 

分 类 号：O157[理学—数学]