2 problems

Let $G$ be a graph with $|V(G)|\ge 2$, let $z_0\in V(G)$, and let $k$ be a positive integer. Let $p:V(G)\rightarrow Z_k$ satisfy … For each vertex $v$, choose an integer…

Let $G$ be a graph, let $k$ be an integer with $k\ge 3$, and let $p:V(G)\rightarrow Z_k$ satisfy … A $p$-orientation is an orientation satisfying the prescribed modulo-$k$ out-degr…