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

三类有向三元系之间关系的一种猜想(英文)

作　　者：田子红 康庆德 

机构地区：[1]Institute of Mathematics, Hebei Normal University

出　　处：《Journal of Mathematical Research and Exposition》2008年第4期769-778,共10页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10671055)

摘　　要：A Mendelsohn (directed, or hybrid) triple system of order v, denoted by MTS(v,λ) (DTS(v,λ), or HTS(v,λ)), is a pair (X,B) where X is a v-set and B is a collection of some cyclic (transitive, or cyclic and transitive) triples on X such that every ordered pair of X belongs to λ triples of B. In this paper, a relation between three types of oriented triple systems was discussed. We conjecture: the block-incident graph of MTS(v,λ) is 3-edge colorable. Then we obtain three disjoint DTS(v,λ)s and four disjoint HT...A Mendelsohn (directed, or hybrid) triple system of order v, denoted by MTS(v,λ) (DTS(v,λ), or HTS(v,λ)), is a pair (X,B) where X is a v-set and B is a collection of some cyclic (transitive, or cyclic and transitive) triples on X such that every ordered pair of X belongs to λ triples of B. In this paper, a relation between three types of oriented triple systems was discussed. We conjecture: the block-incident graph of MTS(v,λ) is 3-edge colorable. Then we obtain three disjoint DTS(v,λ)s and four disjoint HTS(v,λ)s from a given MTS(v,λ).

关 键 词：cyclic triple transitive triple oriented triple system. 

分 类 号：O157.5[理学—数学]