Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Depths of Powers of Edge Ideals   Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we
provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and
compute this limit explicitly. This bound is always achieved if $G$ has no
cycles of length $4$ and every its connected component is either a tree or a
unicyclic graph.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga