Recently the authors [CCLMST23] introduced the notion of shortcut partition of planar graphs and obtained several results from the partition, including a tree cover with $O(1)$ trees for planar metrics and an additive embedding into small treewidth graphs. In this note, we apply the same partition to resolve the Steiner point removal (SPR) problem in planar graphs: Given any set $K$ of terminals in an arbitrary edge-weighted planar graph $G$, we construct a minor $M$ of $G$ whose vertex set is $K$, which preserves the shortest-path distances between all pairs of terminals in $G$ up to a constant factor. This resolves in the affirmative an open problem that has been asked repeatedly in literature.

翻译：最近，作者[CCLMST23]引入了平面图捷径划分的概念，并基于该划分获得了若干结果，包括平面度量的$O(1)$棵树覆盖以及向小树宽图的可加性嵌入。本文中，我们应用同样的划分来解决平面图中的斯坦纳点移除（SPR）问题：给定任意边加权平面图$G$中的终端集合$K$，我们构造$G$的一个子式$M$，其顶点集为$K$，且能保留$G$中所有终端对之间的最短路径距离（至多常数倍）。这肯定性地解决了文献中反复提出的一个开放问题。