Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Morse Theory on Digraphs   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.

37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph