Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DNA Origami and Unknotted A-trails in Torus Graphs   Motivated by the problem of determining unknotted routes for the scaffolding
strand in DNA origami self-assembly, we examine existence and knottedness of
A-trails in graphs embedded on the torus. We show that any A-trail in a
checkerboard-colorable torus graph is unknotted and characterize the existence
of A-trails in checkerboard-colorable torus graphs in terms of pairs of
quasitrees in associated embeddings. Surface meshes are frequent targets for
DNA nanostructure self-assembly, and so we study both triangular and
rectangular torus grids. We show that, aside from one exceptional family, a
triangular torus grid contains an A-trail if and only if it has an odd number
of vertices, and that such an A-trail is necessarily unknotted. On the other
hand, while every rectangular torus grid contains an unknotted A-trail, we also
show that any torus knot can be realized as an A-trail in some rectangular
grid. Lastly, we use a gluing operation to construct infinite families of
triangular and rectangular grids containing unknotted A-trails on surfaces of
arbitrary genus. We also give infinite families of triangular grids containing
no unknotted A-trail on surfaces of arbitrary nonzero genus.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex