Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar Drawings of Higher-Genus Graphs   In this paper, we give polynomial-time algorithms that can take a graph G
with a given combinatorial embedding on an orientable surface S of genus g and
produce a planar drawing of G in R^2, with a bounding face defined by a
polygonal schema P for S. Our drawings are planar, but they allow for multiple
copies of vertices and edges on P's boundary, which is a common way of
visualizing higher-genus graphs in the plane. Our drawings can be defined with
respect to either a canonical polygonal schema or a polygonal cutset schema,
which provides an interesting tradeoff, since canonical schemas have fewer
sides, and have a nice topological structure, but they can have many more
repeated vertices and edges than general polygonal cutsets. As a side note, we
show that it is NP-complete to determine whether a given graph embedded in a
genus-g surface has a set of 2g fundamental cycles with vertex-disjoint
interiors, which would be desirable from a graph-drawing perspective.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas