AI 中文总结
研究k个无根二叉系统发育树共享公共诱导二叉子树的叶子数上界问题，给出新上界为四次迭代指数函数，得到h(k)的四次迭代指数上界并给出指数下界。
AI 中文摘要
Snir和Yuster提出问题，求使得k个无根二叉系统发育树在相同的h(k)个叶子上总能共享一个公共四重奏的最小数h(k)。本文给出了最大一致子树问题的k树版本中叶子数的新上界，即k个无根二叉系统发育树总能在n个叶子上共享一个公共诱导二叉子树的叶子数上界，是一个四次迭代指数函数。这意味着h(k)有一个四次迭代指数上界，还给出了h(k)的指数下界。
英文摘要
Snir and Yuster [Discrete Appl. Math. 347 (2026) 160--171] asked for the least number $h(k)$ such that $k$ unrooted binary phylogenetic trees on the same $h(k)$ leaves always share a common quartet. We give a new upper bound for the $k$-tree version of the Maximum Agreement Subtree problem, namely an upper bound for the number of leaves, on which $k$ unrooted binary phylogenetic trees always share a common induced binary subtree on $n$ leaves, which is a four-times iterated exponential function. For $h(k)$, this implies a four-times iterated exponential upper bound. We also set an exponential lower bound for $h(k)$.
