| 田子红,康庆德.三类有向三元系之间关系的一种猜想[J].数学研究及应用,2008,28(4):769~778 |
| 三类有向三元系之间关系的一种猜想 |
| A Conjecture on the Relation between Three Types of Oriented Triple Systems |
| 投稿时间：2006-12-07 修订日期：2007-03-23 |
| DOI：10.3770/j.issn:1000-341X.2008.04.004 |
| 中文关键词: 循环三元组 可迁三元组 有向三元系. |
| 英文关键词:cyclic triple transitive triple oriented triple system. |
| 基金项目:国家自然科学基金(No.10671055). |
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| 中文摘要: |
| 一个Mendelsohn (Directed, 或Hybrid)三元系 MTS$(v, \lambda)$~(DTS$(v, \lambda)$,或HTS$(v,\lambda))$, 是由$v$元集$X$ 上的一些循环（可迁，或循环和可迁）三元组(简称区组)构成的集合${\cal B}$, 使得$X$上每个由不同元素组成的有序对都恰在 ${\cal B}$的$\lambda$个区组中出现.本文主要讨论了这三类有向三元系之间的一种关联关系，给出猜想：任意MTS$(v,\lambda)$的区组关联图$G(\ |
| 英文摘要: |
| A Mendelsohn (directed, or hybrid) triple system of order $v$, denoted by $\MTS(v, \lambda)$ $(\DTS(v, \lambda)$, or $\HTS(v,\lambda))$, is a pair $(X, {\cal B})$ where $X$ is a $v$-set and ${\cal B}$ is a collection of some cyclic (transitive, or cyclic and transitive) triples on $X$ such that every ordered pair of $X$ belongs to $\lambda$ triples of ${\cal B}$. In this paper, a relation between three types of oriented triple systems was discussed. We conjecture: the block-incident graph of $\MTS(v,\lambda)$ is 3-edge colorable. Then we obtain three disjoint $\DTS(v,\lambda)$s and four disjoint $\HTS(v,\lambda)$s from a given $\MTS(v,\lambda)$. |
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