Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Properties of Numbers of Plane Graphs   We explore various techniques for counting the number of straight-edge
crossing-free graphs that can be embedded on a planar point set. In particular,
we derive a lower bound on the ratio of the number of such graphs with $m+1$
edges to the number of graphs with $m$ edges. We show how a relatively small
improvement of this bound would improve existing bounds concerning numbers of
plane graphs with a prescribed number of edges. Furthermore, we use a
cross-graph charging scheme to derive lower bounds for the number of such
graphs when the point set has few extreme points.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg