Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein homogeneous subrings of graphs   Let $G=(V,E)$ be a connected simple graph, with $n$ vertices such that $S$ is
its homogeneous monomial subring. We prove that if $S$ is normal and
Gorenstein, then $G$ is unmixed with cover number $\lceil\frac{n}{2}\rceil$ and
$G$ has a strong $\lceil\frac{n}{2}\rceil$-$\tau$-reduction. Furthermore, if
$n$ is even, then we show that $G$ is bipartite. Finally, if $S$ is normal and
$G$ is unmixed whose cover number is $\lceil\frac{n}{2}\rceil$, we give
sufficient conditions for $S$ to be Gorenstein.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: stat