Merge trees in discrete Morse theory
Algebraic Topology
2020-07-21 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.2007.10272,
title = {Merge trees in discrete Morse theory},
author = {Benjamin Johnson and Nicholas A. Scoville},
journal= {arXiv preprint arXiv:2007.10272},
year = {2020}
}