3 problems

For every integer $n\ge 1$, determine the exact value of…

For every integer $t\ge 1$, every oriented tree $T$ with $t$ edges, and every loopless digraph $D$ on $n$ vertices with no repeated arcs, if opposite arcs are permitted, $D$ is Eul…

For every $\varepsilon>0$, there exists a constant $C_0>0$ such that, for every digraph $H$ with $h$ arcs and no isolated vertices, every $n$-vertex digraph $D$ satisfying…