Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nordhaus-Gaddum type inequality for the fractional matching number of a
  graph   The fractional matching number of a graph G, is the maximum size of a
fractional matching of G. The following sharp lower bounds for a graph G of
order n are proved, and all extremal graphs are characterized in this paper.
(1)The sum of the fractional matching number of a graph G and the fractional
matching number of its complement is not less than n/2 , where n is not less
than 2. (2) If G and its complement are non-empty, then the sum of the
fractional matching number of a graph G and the fractional matching number of
its complement is not less than (n+1)/2, where n is not less than 28. (3) If G
and its complement have no isolated vertices, then the sum of the fractional
matching number of a graph G and the fractional matching number of its
complement is not less than (n+4)/2, where n is not less than 28.

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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph