Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of Powers of Bipartite Graphs   Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge
ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for
bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is
the graph associated with the polarization of the ideal $(I(G)^{s+1} :
e_1\cdots e_s)$, where $e_1,\ldots e_s$ are edges of $G$. Using these results,
we explicitly compute reg$(I(G)^s)$ for several subclasses of bipartite graphs.

11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol