随机锦标赛中的反直觉相关性
A counter-intuitive correlation in a random tournament
摘要：
考虑一个随机定向图$G=(V,E)$，并设$a$、$s$和$b$是$V$中的三个不同顶点。我们研究事件$\{a\to s\}$和$\{s\to b\}$之间的相关性。我们表明，当$G$是完全图$K_n$，相关性是负的$n=3$，零$n=4$，而且，反直觉，它是积极的$n\ge 5$。我们还表明，相关性总是负的$G$是一个循环，$C_n$，负或零时$G$是一棵树（或森林）。
英文摘要：
Consider a randomly oriented graph $G=(V,E)$ and let $a$, $s$ and $b$ be three distinct vertices in $V$. We study the correlation between the events $\{a\to s\}$ and $\{s\to b\}$. We show that, when $G$ is the complete graph $K_n$, the correlation is negative for $n=3$, zero for $n=4$, and that, counter-intuitively, it is positive for $n\ge 5$. We also show that the correlation is always negative when $G$ is a cycle, $C_n$, and negative or zero when $G$ is a tree (or a forest).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
