三类有向三元系之间关系的一种猜想

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(\

A Conjecture on the Relation between Three Types of Oriented Triple Systems

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 $\MTS(v,\lambda)$.