3 problems

Fix $d\geq 2$, and let $H=\ovar{G}(n,d)$ be the sparse random digraph used in the paper. Write $\ovar{r_1}(H)$ for its one-color oriented Ramsey number. Linear random-digraph conje…

Let $D(n,p)$ be the random directed graph and $G(n,p)$ the random graph, with $p=n^{-1}+\lambda n^{-4/3}$. Let $X^\lambda=n^{-2/3}|\mathcal{C}_1(G(n,p))|$ and…

Let $D\sim\mathcal D(n,p)$ be a random directed graph on vertex set $[n]$, where each possible arc is present independently with probability $p$, and let $C$ be a Hamilton cycle wi…