4 problems

Let $T_k$ be the transitive tournament on $k$ vertices, and let $H_k$ be its $1$-subdivision, obtained by subdividing every arc exactly once. For an oriented graph $H$, let…

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…

For $k,\Delta\geq 1$ and $n>\Delta$, let $H_{k,n,\Delta}$ be an acyclic digraph with $n$ vertices and maximum degree $\Delta$ maximizing $\ovar{r_k}(H)$. Quantitative growth conjec…

For $k,\Delta\geq 1$ and $n>\Delta$, let $H_{k,n,\Delta}$ be an acyclic digraph with $n$ vertices and maximum degree $\Delta$ maximizing $\ovar{r_k}(H)$. Super-polynomial growth co…