Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poly-free constructions for right-angled Artin groups   We show that every right-angled Artin group AG defined by a graph G of finite
chromatic number is poly-free with poly-free length bounded between the clique
number and the chromatic number of G. Further, a characterization of all
right-angled Artin groups of poly-free length 2 is given, namely the group AG
has poly-free length 2 if and only if there exists an independent set of
vertices D in G such that every cycle in G meets D at least twice. Finally, it
is shown that AG is a semidirect product of 2 free groups of finite rank if and
only if G is a finite tree or a finite complete bipartite graph. All of the
proofs of the existence of poly-free structures are constructive.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con