Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cone of weighted graphs generated by triangles   Motivated by problems involving triangle-decompositions of graphs, we examine
the facet structure of the cone $\tau_n$ of weighted graphs on $n$ vertices
generated by triangles. Our results include enumeration of facets for small
$n$, a construction producing facets of $\tau_{n+1}$ from facets of $\tau_n$,
and an arithmetic condition on entries of the normal vectors. We also point out
that a copy of $\tau_n$ essentially appears via the perimeter inequalities at
one vertex of the metric polytope.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph