论文标题
按得分序列对本质上的链接比赛进行分类
Classifying Intrinsically Linked Tournaments by Score Sequence
论文作者
论文摘要
在8个或更多顶点上的比赛可能本质上链接为有向图。我们通过检查其得分序列开始对本质上联系的比赛的分类。尽管许多不同的比赛可能具有相同的得分序列，但存在得分序列$ s $，因此任何具有得分序列$ s $的比赛都有一个嵌入，没有一个始终定向的链接。我们称此类得分序列$ \ textit {cintless} $，我们证明了8个顶点锦标赛的绝大多数得分序列都是无连锁的。 我们还将这些结果扩展到$ n $顶点锦标赛，并能够对许多更长的得分序列进行分类。我们表明，对于任何$ n $，至少存在$ o（n）$无连接得分序列，但是我们认为，随着$ n $变大，无链接的长度$ n $的得分序列的比例为0。
A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequences. While many distinct tournaments may have the same score sequence, there exist score sequences $S$ such that any tournament with score sequence $S$ has an embedding with no nonsplit consistently oriented link. We call such score sequences $\textit{linkless}$, and we show that the vast majority of score sequences for 8 vertex tournaments are linkless. We also extend these results to $n$ vertex tournaments and are able to classify many longer score sequences as well. We show that for any $n$, there exist at least $O(n)$ linkless score sequences, but we conjecture that the fraction of score sequences of length $n$ that are linkless goes to 0 as $n$ becomes large.
