论文标题
$ \ {p，q \} $ - 方向的存在在边缘连接图中
The existence of $\{p,q\}$-orientations in edge-connected graphs
论文作者
论文摘要
1976年，弗兰克（Frank）和gy {á} rf {á} s在任意图$ g $中存在方向的必要条件，使每个顶点$ v $，$ d^+_ g（v）的每个顶点$ d^+_ g（v）的$ p（v）$ p（v） $ v（g）$上的整数值函数，带有$ p \ le q $。在本文中，我们给出了足够的边缘连接性条件，以在$ g $中存在一个方向，以使每个顶点$ v $，$ d^+_ g（v）\ in \ {p（v），q（v）\} $，规定每个vertex $ v $ v $，$ p（v） q（v）$，$ | q（v）-p（v）| \ le k $，并且有$ t（v）\ in \ {p（v），q（v）\} $，其中$ | e（g）| = \ sum_ {v \ in v（g）} t（v）t（v）$。该结果是由于Thomassen（2012）在高度边缘连接图中存在模量方向而引起的定理的概括。
In 1976 Frank and Gy{á}rf{á}s gave a necessary and sufficient condition for the existence of an orientation in an arbitrary graph $G$ such that for each vertex $v$, the out-degree $d^+_G(v)$ of it satisfies $p(v)\le d^+_G(v)\le q(v)$, where $p$ and $q$ are two integer-valued functions on $V(G)$ with $p\le q$. In this paper, we give a sufficient edge-connectivity condition for the existence of an orientation in $G$ such that for each vertex $v$, $d^+_G(v)\in \{p(v),q(v)\}$, provided that for each vertex $v$, $p(v)\le \frac{1}{2}d_G(v) \le q(v)$, $|q(v)-p(v)|\le k$, and there is $t(v)\in \{p(v),q(v)\}$ in which $|E(G)|=\sum_{v\in V(G)}t(v)$. This result is a generalization of a theorem due to Thomassen (2012) on the existence of modulo orientations in highly edge-connected graphs.
