论文标题
树刺不是单调的
The Tree Stabbing Number is not Monotone
论文作者
论文摘要
令$ p \ subseteq \ mathbb {r}^2 $是一组点，$ t $是$ p $的跨度树。 $ t $的\ emph {刺伤号}是飞机中任何线路中的最大交叉点，用$ t $的边缘确定。 $ p $的\ emph {树刺数}是$ p $的任何生成树的最小刺伤数。我们证明，树刺是一个单调参数，即存在点设置$ p \ subsetneq p'$，以至于\ treestab {$ p $} $> $ \ treestab {$ p'$ p'$}，回答eppstein \ cite \ cite \ cite \ cite \ cite [open worge 〜17.5.5] eppStein_2018}。
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}.
