刺树数不是单调的
The Tree Stabbing Number is not Monotone
摘要：
设$P \subseteq \mathbb{R}^2$是点的集合，并且$T$是$P$的生成树。$T$的\emph{stabbing number}是平面中任何直线与$T$的边确定的最大相交数。$P$的\emph{tree stabbing number}是$P$的任何生成树的最小穿刺数。我们证明了树刺数不是单调参数，即，存在点集$P \subsetneq P'$，使得\treestab{$P$} $>$ \treestab{$P'$}，回答Eppstein的问题\cite [未决问题~17.5]{eppstein_2018}。
英文摘要：
Let $P \subseteq \mathbb{R}^2$ be a set of points and $T$ be a spanning tree of $P$. The \emph{stabbing number} of $T$ is the maximum number of intersections any line in the plane determines with the edges of $T$. The \emph{tree stabbing number} of $P$ is the minimum stabbing number of any spanning tree of $P$. We prove that the tree stabbing number is not a monotone parameter, i.e., there exist point sets $P \subsetneq P'$ such that \treestab{$P$} $>$ \treestab{$P'$}, answering a question by Eppstein \cite[Open Problem~17.5]{eppstein_2018}.
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。
