A necessary and sufficient condition for the existence of $\{p,p+1,q-1,q\}$-orientations in simple graphs

Morteza Hasanvand

Let $G$ be a simple graph and let $p$ and $q$ be two integer-valued functions on $V(G)$ with $p<q$ in which for each $v\in V(G)$, $q(v)\ge \frac{1}{2}{d}_G(v)$ and $p(v) \ge \frac{…