论文标题
$ \ {p，p+1，q-1，q \} $ - 方向的必要条件
A necessary and sufficient condition for the existence of $\{p,p+1,q-1,q\}$-orientations in simple graphs
论文作者
论文摘要
让$ g $是一个简单的图表，让$ p $和$ q $是$ v（g）$上的两个整数值函数，其中$ p <q $，其中每个$ v \ in v（g）$，$ q（v）\ ge \ ge \ frac {1} {1} {2} {2} {2} {2} d_g（v）$ p（v）$ p（v）$ p（v）$ p（v）在本说明中，我们表明$ g $具有一个方向，以至于每个顶点$ v $，$ d^+_ g（v）\ in \ {p（v），p（v）+1，q（v）-1，q（v）-1，q（v）\ q（v）\ y n且仅在为每个vertex $ v $ v $ p（$ p d^）中提供方向， $ d^+_ g（v）$表示$ g $中的$ v $的超级度。从这个结果中，我们在两分的简单图中，在两分的简单图中，我们完善了结果。
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 $p(v) \ge \frac{1}{2} q(v)-2$. In this note, we show that $G$ has an orientation such that for each vertex $v$, $d^+_G(v)\in\{p(v),p(v)+1,q(v)-1,q(v)\}$ if and only if it has an orientation such that for each vertex $v$, $p(v) \le d^+_G(v)\le q(v)$ where $d^+_G(v)$ denotes the out-degree of $v$ in $G$. From this result, we refine a result due to Addario-Berry, Dalal, and Reed (2008) in bipartite simple graphs on the existence of degree constrained factors.
