Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On ribbon graphs and virtual links   We introduce a new equivalence relation on decorated ribbon graphs, and show
that its equivalence classes directly correspond to virtual links. We
demonstrate how this correspondence can be used to convert any invariant of
virtual links into an invariant of ribbon graphs, and vice versa.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th