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| 五点八边图的完美T(G)-三元系 | |
| 引用本文： | 侯英涛,康庆德,张艳丽. 五点八边图的完美T(G)-三元系[J]. 应用数学学报, 2011, 34(5) |
| 作者姓名： | 侯英涛 康庆德 张艳丽 |
| 作者单位： | 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 |
| 基金项目： | 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Kn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3Kn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Kn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K4的所有子图及K5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. |
| 关 键 词： | T(G) T(G)-三元系 完全T(G)-三元系 |
Perfect T(G)-triple System for Each Subgraph G of K_5 with Eight Edges |
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| HOU YINGTAO , KANG QINGDE , ZHANG YANLI. Perfect T(G)-triple System for Each Subgraph G of K_5 with Eight Edges[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(5) | |
| Authors: | HOU YINGTAO KANG QINGDE ZHANG YANLI |
| Affiliation: | HOU YINGTAO (Basic Teaching Department,North China Baoding Electric Power Voc.& Tech.College,Baoding 071051) KANG QINGDE (Institute of Mathematics,Hebei Normal University,Shijiazhuang 050016) ZHANG YANLI (Department of Science and Technology,Huaxin College,Shijiazhuang University of Economics,Shijiazhuang 050091) |
| Abstract: | Let G be a subgraph of K_n.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 3K_n into copies of T(G) is called a T(G)-triple system of order n.If,in each copy of T(G) in a T(G)-triple system,one edge is taken from each 3-cycle(chosen so that these edges form a copy of G) in such a way that the resulting copies of G form an edge-disjoint decomposition of K_n,then th... |
| Keywords: | T(G) T(G)-triple system perfect T(G)-triple system |
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