利用边不相交路径逃离网格角点
Escaping from the corner of a grid by edge disjoint paths
摘要：
设$Q$是平面上整数格$G$的有限子图，$T$是$G$中不同顶点对的集合，称为“终端对”。从$Q$逃逸子集$X\subset T\cap Q$意味着找到从$X$中的终端到$Q$的边界中的集合$L$的不同顶点的边不相交路径。这里我们证明了几个引理的情况下，$Q$是一个$3\times 3$网格，$L$是一个垂直和水平的边界线的$Q$的并集，此外，$T$是一个集的四个终端对在$G$，使$|T\cap Q|\geq 5$。这些引理在[4]中得到了应用，并完成了两条（单向）无限路的笛卡儿积具有路对数4的证明。
英文摘要：
Let $Q$ be a finite subgraph of the integer grid $G$ in the plane, and let $T$ be a set of pairs of distinct vertices in $G$, called `terminal pairs'. Escaping a subset $X\subset T\cap Q$ from $Q$ means finding edge disjoint paths from the terminals in $X$ into distinct vertices of a set $L$ in the boundary of $Q$. Here we prove several lemmas for the cases where $Q$ is a $3\times 3$ grid, $L$ is the union of a vertical and horizontal boundary line of $Q$, furthermore, $T$ is a set of four terminal pairs in $G$ such that $|T\cap Q|\geq 5$. These lemmas are applied in [4] and complete the proof that the Cartesian product of two (one way) infinite paths has path-pairability number four.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
