有关偏序集与竞赛图的讨论

A note on posets and tournaments

给定一个竞赛图T=(V,A),与T相关联的偏序集P是一个偏序集P:=(V, ),使得 x,y∈V(T),x y当且仅当x=y或者d(x,y)≥3.证明了每一个竞赛图都与一个偏序集相关联,但存在偏序集不与任何竞赛图相关联.此外,还对与竞赛图相关联的偏序集的性质进行了讨论.

Given a tournament T=(V,A), the associated poset P of T is a poset P∶=(V,) such that x,y∈V, xy if and only if x=y or d(x,y)≥3. In this article, it shows that every tournament is associated with a poset, but there exist posets which are not (associated) with any tournament. And some remarks on posets which are associated with tournament are given in this paper.