Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The monomial ideal of independent sets associated to a graph   Independent sets play a key role into the study of graphs and important
problems arising in graph theory reduce to them. We define the monomial ideal
of independent sets associated to a finite simple graph and describe its
homological and algebraic invariants in terms of the combinatorics of the
graph. We compute the minimal primary decomposition and characterize the
Cohen--Macaulay ideals. Moreover, we provide a formula for computing the Betti
numbers, which depends only on the coefficients of the independence polynomial
of the graph.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci