2 problems

Let $G$ be a loopless graph, and let $d(v)$ denote the degree of each vertex $v\in V(G)$. Given a function $F:V(G)\to 2^{\mathbb N}$, an orientation is $F$-avoiding if its out-degr…

Let $G$ be a loopless $d$-regular graph, with parallel edges permitted, and let $F\subseteq\{0,1,\ldots,d\}$ be a list of forbidden out-degrees. An orientation is $F$-avoiding if n…