Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Number of Cycles in a Graph   There is a sizable literature on investigating the minimum and maximum
numbers of cycles in a class of graphs. However, the answer is known only for
special classes. This paper presents a result on the smallest number of cycles
in hamiltonian 3-connected cubic graphs. Further, it describes a proof
technique that could improve an upper bound of the largest number of cycles in
a hamiltonian graph.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg