Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stable set polytope of ($P_6$,triangle)-free graphs and new
  facet-inducing graphs   The stable set polytope of a graph $G$, denoted as STAB($G$), is the convex
hull of all the incidence vectors of stable sets of $G$. To describe a linear
system which defines STAB($G$) seems to be a difficult task in the general
case. In this paper we present a complete description of the stable set
polytope of ($P_6$,triangle)-free graphs (and more generally of
($P_6$,paw)-free graphs). For that we combine different tools, in the context
of a well known result of Chv\'atal \cite{Chvatal1975} which allows to focus
just on prime facet-inducing graphs, with particular reference to a structure
result on prime ($P_6$,triangle)-free graphs due to Brandst\"adt et al.
\cite{BraKleMah2005}. Also we point out some peculiarities of new
facet-inducing graphs detected along this study with the help of a software.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con