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arXiv · 2007.10272

Merge trees in discrete Morse theory

Benjamin Johnson·Nicholas A. Scoville
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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.

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Benjamin Johnson, Nicholas A. Scoville. 2020-07-20. Merge trees in discrete Morse theory. https://arxiv.org/abs/2007.10272

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