Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of Planar Embeddability of Trees inside Simple Polygons   Geometric embedding of graphs in a point set in the plane is a well known
problem. In this paper, the complexity of a variant of this problem, where the
point set is bounded by a simple polygon, is considered. Given a point set in
the plane bounded by a simple polygon and a free tree, we show that deciding
whether there is a planar straight-line embedding of the tree on the point set
inside the simple polygon is NP-complete. This implies that the straight-line
constrained point-set embedding of trees is also NP-complete, which was posed
as an open problem in [8].

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys