Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence criterion of such a cycle that the set of vertices beyond the
  cycle is independent   We prove that every 2-connected graph with $\delta(G) \geqslant \frac{v(G) +
2}{3}$ has such a cycle that the set of vertices beyond the cycle is
independent.

6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio