Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Girth six cubic graphs have Petersen minors   We prove that every 3-regular graph with no circuit of length less than six
has a subgraph isomorphic to a subdivision of the Petersen graph.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas