论文标题
在竞争指数和多部分比赛的时期
On competition indices and periods of multipartite tournaments
论文作者
论文摘要
在本文中，我们计算竞争指数和多部分比赛的时期。我们首先表明，无环digraph $ d $的竞争期是一个，$ζ（d） +1 $是$ d $ $ζ（d）$的竞争指数的尖锐上限，是$ d $的水槽消除指数。然后，我们证明，特别是对于无环$ k $ - 明确锦标赛$ d $，$ d $的竞赛指数是$ζ（d）$或$ζ$或$ζ（d） +1 $，用于整数$ k \ ge 3 $。通过开发有用的工具来从给定的定向步行中创建一定常规图案的无限定向步行，我们表明，带有水槽和定向周期的多零件比赛的竞赛期最多是三个。我们还证明，原始挖掘的竞争指数不超过其指数。
In this paper, we compute competition indices and periods of multipartite tournaments. We first show that the competition period of an acyclic digraph $D$ is one and $ζ(D) +1$ is a sharp upper bound of the competition index of $D$ where $ζ(D)$ is the sink elimination index of $D$. Then we prove that, especially, for an acyclic $k$-partite tournament $D$, the competition index of $D$ is $ζ(D)$ or $ζ(D) +1$ for an integer $k \ge 3$. By developing useful tools to create infinitely many directed walks in a certain regular pattern from given directed walks, we show that the competition period of a multipartite tournament with sinks and directed cycles is at most three. We also prove that the competition index of a primitive digraph does not exceed its exponent.
