Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flexible placements of graphs with rotational symmetry   We study the existence of an $n$-fold rotationally symmetric placement of a
symmetric graph in the plane allowing a continuous deformation that preserves
the symmetry and the distances between adjacent vertices. We show that such a
flexible placement exists if and only if the graph has a NAC-colouring
satisfying an additional property on the symmetry; a NAC-colouring is a
surjective edge colouring by two colours such that every cycle is either
monochromatic, or there are at least two edges of each colour.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th