Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Zero-Sum Perfect Matchings of Complete Graphs   In this paper, we prove that given a 2-edge-coloured complete graph $K_{4n}$
that has the same number of edges of each colour, we can always find a perfect
matching with an equal number of edges of each colour. This solves a problem
posed by Caro, Hansberg, Lauri, and Zarb. The problem is also independently
solved by Ehard, Mohr, and Rautenbach.

26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an