Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed-Orientation Equilateral Triangle Matching of Point Sets   Given a point set $P$ and a class $\mathcal{C}$ of geometric objects,
$G_\mathcal{C}(P)$ is a geometric graph with vertex set $P$ such that any two
vertices $p$ and $q$ are adjacent if and only if there is some $C \in
\mathcal{C}$ containing both $p$ and $q$ but no other points from $P$. We study
$G_{\bigtriangledown}(P)$ graphs where $\bigtriangledown$ is the class of
downward equilateral triangles (ie. equilateral triangles with one of their
sides parallel to the x-axis and the corner opposite to this side below that
side). For point sets in general position, these graphs have been shown to be
equivalent to half-$\Theta_6$ graphs and TD-Delaunay graphs.
  The main result in our paper is that for point sets $P$ in general position,
$G_{\bigtriangledown}(P)$ always contains a matching of size at least
$\lceil\frac{n-2}{3}\rceil$ and this bound cannot be improved above
$\lceil\frac{n-1}{3}\rceil$.
  We also give some structural properties of $G_{\davidsstar}(P)$ graphs, where
$\davidsstar$ is the class which contains both upward and downward equilateral
triangles. We show that for point sets in general position, the block cut point
graph of $G_{\davidsstar}(P)$ is simply a path. Through the equivalence of
$G_{\davidsstar}(P)$ graphs with $\Theta_6$ graphs, we also derive that any
$\Theta_6$ graph can have at most $5n-11$ edges, for point sets in general
position.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an