Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotone Paths in Geometric Triangulations   (I) We prove that the (maximum) number of monotone paths in a geometric
triangulation of $n$ points in the plane is $O(1.7864^n)$. This improves an
earlier upper bound of $O(1.8393^n)$; the current best lower bound is
$\Omega(1.7003^n)$.
  (II) Given a planar geometric graph $G$ with $n$ vertices, we show that the
number of monotone paths in $G$ can be computed in $O(n^2)$ time.

7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con