多部竞赛图的点泛圈性(英文)

Vertex-pancyclic Multipartite Tournaments

把c 部完全图的每条边任意加上一个方向后得到的定向图称为c 部竞赛图 ,设T为c 部竞赛图 ,定义ig(T) =maxx ,y∈VCT|d+(x) -d- (y) | .给出了c 部竞赛图具有点泛圈性的一个充分条件 ,即 :设T为c 部竞赛图 (c≥ 13) ,V1 ,V2 ,…Vc 为T的各分部 .如果 |V1 |≤ |V2 |≤…≤ |Vc|≤ |V1 | + 1并且ig(T)≤ 1。

A c partite tournament is an oriented graph obtained from a complete c partite graph. A multipartite tournament is a c partite tournament with c≥2. T being a multipartite tournament, we define i g(T)=max |d +(x)-d -(y)| over all pairs of vertices x,y∈V(T). We prove that if V 1, V 2, ..., V c are the partite sets of a c partite ( c≥3 ) tournament T ,with |V 1|≤|V 2|≤...≤|V 1|+1 and i g(T)≤1, then T is vertex pancyclic.