First critical probability for a problem on random orientations in $G(n,p)$.

摘要

We study the random graph $G(n,p)$ with a random orientation. For three fixed vertices $s,a,b$ in $G(n,p)$ we study the correlation of the events ${ao s}$ (there exists a directed path from $a$ to $s$) and ${so b}$. We prove that asymptotically the correlation is negative for small $p$, $p