Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on graph drawings with star-shaped boundaries in the plane   In this note, we propose a straightforward method to produce an straight-line
embedding of a planar graph where one face of a graph is fixed in the plane as
a star-shaped polygon. It is based on minimizing discrete Dirichlet energies,
following the idea of Tutte's embedding theorem. We will call it a geodesic
triangulation of the star-shaped polygon. Moreover, we study the homotopy
property of spaces of all straight-line embeddings. We give a simple argument
to show that this space is contractible if the boundary is a non-convex
quadrilateral. We conjecture that the same statement holds for general
star-shaped polygons.

29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ