Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Drawings of Kn with the same rotation scheme are the same up to
  Reidemeister moves. Gioan's Theorem   A {\em good drawing\/} of $K_n$ is a drawing of the complete graph with $n$
vertices in the sphere such that: no two edges with a common end cross; no two
edges cross more than once; and no three edges all cross at the same point.
Gioan's Theorem asserts that any two good drawings of $K_n$ that have the same
rotations of incident edges at every vertex are equivalent up to Reidemeister
moves. At the time of preparation, 10 years had passed between the statement in
the WG 2005 conference proceedings and our interest in the proposition. Shortly
after we completed our preprint, Gioan independently completed a preprint.

4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph