Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximum number of cycles in a graph with fixed number of edges   The main topic considered is maximizing the number of cycles in a graph with
given number of edges. In 2009, Kir\'aly conjectured that there is constant $c$
such that any graph with $m$ edges has at most $(1.4)^m$ cycles. In this paper,
it is shown that for sufficiently large $m$, a graph with $m$ edges has at most
$(1.443)^m$ cycles. For sufficiently large $m$, examples of a graph with $m$
edges and $(1.37)^m$ cycles are presented. For a graph with given number of
vertices and edges an upper bound on the maximal number of cycles is given.
Also, exponentially tight bounds are proved for the maximum number of cycles in
a multigraph with given number of edges, as well as in a multigraph with given
number of vertices and edges.

31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ