Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graph theoretical Poincare-Hopf Theorem   We introduce the index i(v) = 1 - X(S(v)) for critical points of a locally
injective function f on the vertex set V of a simple graph G=(V,E). Here S(v) =
{w in E | (v,w) in E, f(w)-f(v)<0} is the subgraph of the unit sphere at v in
G. It is the exit set of the gradient vector field. We prove that the sum of
i(v) over V is always is equal to the Euler characteristic X(G) of the graph G.
This is a discrete Poincare-Hopf theorem in a discrete Morse setting. It allows
to compute X(G) for large graphs for which other methods become impractical.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn