Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved bounds for the shortness coefficient of cyclically 4-edge
  connected cubic graphs and snarks   We present a construction which shows that there is an infinite set of
cyclically 4-edge connected cubic graphs on $n$ vertices with no cycle longer
than $c_4 n$ for $c_4=\frac{12}{13}$, and at the same time prove that a certain
natural family of cubic graphs cannot be used to lower the shortness
coefficient $c_4$ to 0.
  The graphs we construct are snarks so we get the same upper bound for the
shortness coefficient of snarks, and we prove that the constructed graphs have
an oddness growing linearly with the number of vertices.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ