Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The intersection graph of the disks with diameters the sides of a convex
  $n$-gon   Given a convex polygon of $n$ sides, one can draw $n$ disks (called side
disks) where each disk has a different side of the polygon as diameter and the
midpoint of the side as its center. The intersection graph of such disks is the
undirected graph with vertices the $n$ disks and two disks are adjacent if and
only if they have a point in common. We prove that for every convex polygon
this graph is planar. Particularly, for $n=5$, this shows that for any convex
pentagon there are two disks among the five side disks that do not intersect,
which means that $K_5$ is never the intersection graph of such five disks. For
$n=6$, we then have that for any convex hexagon the intersection graph of the
side disks does not contain $K_{3,3}$ as subgraph.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat