Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Associated primes of powers of edge ideals and ear decompositions of
  graphs   In this paper, we give a complete description of the associated primes of
every power of the edge ideal in terms of generalized ear decompositions of the
graph. This result establishes a surprising relationship between two seemingly
unrelated notions of Commutative Algebra and Combinatorics. It covers all
previous major results in this topic and has several interesting consequences.

11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg