Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the minimum order of a quadrangulation on a given closed 2-manifold   A partial formula is provided to calculate the smallest number of vertices
possible in a quadrangulation on the closed orientable 2-manifold of given
genus. This extends the previously known partial formula due to N. Hartsfield
and G. Ringel [J. Comb. Theory, Ser. B, 1989, 46, 84-95].

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg