论文标题
在离散的摩尔斯理论中合并树木
Merge trees in discrete Morse theory
论文作者
论文摘要
在本文中，我们研究了树上离散的摩尔斯功能引起的合并树木。给定离散的摩尔斯函数，我们提供了一种构建诱导的合并树的方法，并根据诱导的合并树定义了离散摩尔斯函数等效的新概念。然后，我们将树的匹配数与诱导的合并树的某个不变性联系起来。最后，我们计算可以在恒星图上诱导的合并树的数量并表征诱导的合并树。
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse functions based on the induced merge tree. We then relate the matching number of a tree to a certain invariant of the induced merge tree. Finally, we count the number of merge trees that can be induced on a star graph and characterize the induced merge tree.
