Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Depth stability of edge ideals   Let $G$ be a connected finite simple graph and let $I_G$ be the edge ideal of
$G$. The smallest number $k$ for which $\depth S/I_G^k$ stabilizes is denoted
by $\dstab(I_G)$. We show that $\dstab(I_G)<\ell(I_G)$ where $\ell(I_G)$
denotes the analytic spread of $I$. For trees we give a stronger upper bound
for $\dstab(I_G)$. We also show for any two integers $1\leq a<b$ there exists a
tree for which $\dstab(I_G)=a$ and $\ell(I_G)=b$.

24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci