Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Associated primes of powers of edge ideals   Let G be a graph and let I be its edge ideal. Our main result shows that the
sets of associated primes of the powers of I form an ascending chain. It is
known that the sets of associated primes of I(i) and intcl(I(i)) stabilize for
large i, where "intcl" denotes integral closure and I(i) denotes the i-th power
of I. We show that for edge ideals their corresponding stable sets are equal.
To show our main result we use a classical result of Berge from matching theory
and certain notions from combinatorial optimization.

7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph