Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lower bound on the order of the largest induced forest in planar
  graphs with high girth   We give here new upper bounds on the size of a smallest feedback vertex set
in planar graphs with high girth. In particular, we prove that a planar graph
with girth $g$ and size $m$ has a feedback vertex set of size at most
$\frac{4m}{3g}$, improving the trivial bound of $\frac{2m}{g}$. We also prove
that every $2$-connected graph with maximum degree $3$ and order $n$ has a
feedback vertex set of size at most $\frac{n+2}{3}$.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio