Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order-preserving 1-string representations of planar graphs   This paper considers 1-string representations of planar graphs that are
order-preserving in the sense that the order of crossings along the curve
representing vertex $v$ is the same as the order of edges in the clockwise
order around $v$ in the planar embedding. We show that this does not exist for
all planar graphs (not even for all planar 3-trees), but show existence for
some subclasses of planar partial 3-trees. In particular, for outer-planar
graphs it can be order-preserving and outer-string in the sense that all ends
of strings are on the outside of the representation.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th