Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A scaling limit for the length of the longest cycle in a sparse random
  graph   We discuss the length of the longest cycle in a sparse random graph
$G_{n,p},p=c/n$. $c$ constant. We show that for large $c$ there is a function
$f(c)$ such that $L_n(c)/n\to f(c)$ a.s. The function $f(c)=1-\sum_{k=1}^\infty
p_k(c)e^{-kc}$ where $p_k$ is a polynomial in $k$. We are only able to
explicitly give the values $p_1,p_2$, although we could in principle compute
any $p_k$. We see immediately that the length of the longest path is also
asymptotic to $f(c)n$ w.h.p.

9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th