On Merge Trees and Discrete Morse Functions on Paths and Trees release_zm5pgo5gtrabdbnom2io2yxcne

by Julian Brüggemann

Released as a report .

2022  

Abstract

In this work we answer an open question asked by Johnson--Scoville. We show that each merge tree is represented by a discrete Morse function on a path. Furthermore, we present explicit constructions for two different but related kinds of discrete Morse functions on paths that induce any given merge tree. A refinement of the used methods allows us to define notions of equivalence of discrete Morse functions on trees which give rise to a bijection between equivalence classes of discrete Morse functions and isomorphism classes of certain labeled merge trees. We also compare our results to similar ones from the literature, in particular to work by Curry.
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Type  report
Stage   submitted
Date   2022-09-09
Version   v3
Language   en ?
Number  MPIM-Bonn-2021
arXiv  2112.01311v3
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