Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Circumference of Essentially 4-connected Planar Graphs   A planar graph is essentially $4$-connected if it is 3-connected and every of
its 3-separators is the neighborhood of a single vertex. Jackson and Wormald
proved that every essentially 4-connected planar graph $G$ on $n$ vertices
contains a cycle of length at least $\frac{2n+4}{5}$, and this result has
recently been improved multiple times.
  In this paper, we prove that every essentially 4-connected planar graph $G$
on $n$ vertices contains a cycle of length at least $\frac{5}{8}(n+2)$. This
improves the previously best-known lower bound $\frac{3}{5}(n+2)$.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int