Discrete Morse Theory on Digraphs
Yong Lin, Chong Wang, Shing–Tung Yau · arXiv (Cornell University) · 2021
In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using quasi-isomorphism between path complex and discrete Morse complex, we also prove a general sufficient condition for digraphs that the Morse functions satisfying this necessary and sufficient condition.