Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Asymptotic Packing of Geometric Graphs   A set of geometric graphs is {\em geometric-packable} if it can be
asymptotically packed into every sequence of drawings of the complete graph
$K_n$. For example, the set of geometric triangles is geometric-packable due to
the existence of Steiner Triple Systems. When $G$ is the $4$-cycle (or
$4$-cycle with a chord), we show that the set of plane drawings of $G$ is
geometric-packable. In contrast, the analogous statement is false when $G$ is
nearly any other planar Hamiltonian graph (with at most 3 possible exceptions).
A convex geometric graph is {\em convex-packable} if it can be asymptotically
packed into the convex drawings of the complete graphs. For each planar
Hamiltonian graph $G$, we determine whether or not a plane $G$ is
convex-packable. Many of our proofs explicitly construct these packings; in
these cases, the packings exhibit a symmetry that mirrors the vertex
transitivity of $K_n$.

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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th