Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of the Multiplicative 1-2-3 Conjecture   We prove that the product version of the 1-2-3 Conjecture, raised by
Skowronek-Kazi{\'o}w in 2012, is true. Namely, for every connected graph with
order at least 3, we prove that we can assign labels 1,2,3 to the edges in such
a way that no two adjacent vertices are incident to the same product of labels.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int