The Tree Stabbing Number is not Monotone

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}.