Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The neighborhood complex of a random graph   For a graph G, the neighborhood complex N[G] is the simplicial complex having
all subsets of vertices with a common neighbor as its faces. It is a well known
result of Lovasz that if N[G] is k-connected, then the chromatic number of G is
at least k + 3.
  We prove that the connectivity of the neighborhood complex of a random graph
is tightly concentrated, almost always between 1/2 and 2/3 of the expected
clique number. We also show that the number of dimensions of nontrivial
homology is almost always small, O(log d), compared to the expected dimension d
of the complex itself.

24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat