The degree-two vertex conjecture for random tournaments

Let $G=(V,E)$ be a connected graph, and let $a$, $s$, and $b$ be three distinct vertices in $V$. The events $\{a\to s\}$ and $\{s\to b\}$ record directed reachability in the random tournament associated with $G$.

Degree-two vertex conjecture. If $s$ has degree at most two, then the events $\{a\to s\}$ and $\{s\to b\}$ are independent or negatively correlated.

This extends the corresponding result for trees and the established bound for cycles. The claim concerns the sign of the correlation when the distinguished vertex has degree at most two; no resolution is supplied in the source.