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Paper detail

Merge trees in discrete Morse theory

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.

preprint2020arXivOpen access
Benjamin JohnsonNicholas A. Scoville
math.ATmath.CO
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Benjamin JohnsonNicholas A. Scoville

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