Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shortest cycle covers and cycle double covers with large 2-regular
  subgraphs   In this paper we show that many snarks have shortest cycle covers of length
$\frac{4}{3}m+c$ for a constant $c$, where $m$ is the number of edges in the
graph, in agreement with the conjecture that all snarks have shortest cycle
covers of length $\frac{4}{3}m+o(m)$.
  In particular we prove that graphs with perfect matching index at most 4 have
cycle covers of length $\frac{4}{3}m$ and satisfy the $(1,2)$-covering
conjecture of Zhang, and that graphs with large circumference have cycle covers
of length close to $\frac{4}{3}m$. We also prove some results for graphs with
low oddness and discuss the connection with Jaeger's Petersen colouring
conjecture.

3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom