Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycles of given lengths in unicyclic components in sparse random graphs   Let $L$ be subset of $\{3,4,\dots\}$ and let $X_{n,M}^{(L)}$ be the number of
cycles belonging to unicyclic components whose length is in $L$ in the random
graph $G(n,M)$. We find the limiting distribution of $X_{n,M}^{(L)}$ in the
subcritical regime $M=cn$ with $c<1/2$ and the critical regime
$M=\frac{n}{2}\left(1+\mu n^{-1/3}\right)$ with $\mu=O(1)$. Depending on the
regime and a condition involving the series $\sum_{l \in L} \frac{z^l}{2l}$, we
obtain in the limit either a Poisson or a normal distribution as $n\to\infty$.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc