Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random cubic graphs are not homomorphic to the cycle of size 7   We prove that a random cubic graph almost surely is not homomorphic to a
cycle of size 7. This implies that there exist cubic graphs of arbitrarily high
girth with no homomorphisms to the cycle of size 7.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org