Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the extremal Betti numbers of the binomial edge ideal of closed
  graphs   We study the equality of the extremal Betti numbers of the binomial edge
ideal $J_G$ and those of its initial ideal ${\rm in}(J_G)$ of a closed graph
$G$. We prove that in some cases there is an unique extremal Betti number for
${\rm in}(J_G)$ and as a consequence there is an unique extremal Betti number
for $J_G$ and these extremal Betti numbers are equal

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin