Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Saturation and associated primes of powers of edge ideals   For the edge ideal I of an arbitrary simple graph G we describe the monomials
of the saturation of a power of I in terms of (vertex) weighted graphs
associated with the monomials. This description allows us to characterize the
embedded associated primes of a power of I as covers of G which contain certain
types of subgraphs of G. As an application, we completely classify the
associated primes of the second and the third power of I in terms of G.

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The categories of this paper are: hep-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom