On the Number of 5‐Cycles in a Tournament
On the Number of 5‐Cycles in a Tournament
复制标题
关于锦标赛中 5 个周期的数量
作者：
Natasha Komarov;John Mackey
我们找到了一个关于竞赛图中有向5圈数的公式，并使用该公式找到了任何n-竞赛图中5圈数的上界和下界。特别地，我们证明了5圈的最大数目渐近等于34 n5，这是随机竞赛图（p=12）中5圈的期望数目，几乎所有竞赛图都是相等的（达到数量级）。
We find a formula for the number of directed 5‐cycles in a tournament in terms of its edge scores and use the formula to find upper and lower bounds on the number of 5‐cycles in any n‐tournament. In particular, we show that the maximum number of 5‐cycles is asymptotically equal to 34n5 , the expected number 5‐cycles in a random tournament ( p=12 ), with equality (up to order of magnitude) for almost all tournaments.