Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Posa's conjecture for random graphs   The famous Posa conjecture states that every graph of minimum degree at least
2n/3 contains the square of a Hamilton cycle. This has been proved for large n
by Koml\'os, Sark\"ozy and Szemer\'edi. Here we prove that if p >
n^{-1/2+\eps}, then asymptotically almost surely, the binomial random graph
G_{n,p} contains the square of a Hamilton cycle. This provides an `approximate
threshold' for the property in the sense that the result fails to hold if p<
n^{-1/2}.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
1
The categories of this paper are: cs