Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalization of neighborhood complexes   We introduce the notion of r-neighborhood complex for a positive integer r,
which is a natural generalization of Lovasz neighborhood complex. The
topologies of these complexes give some obstructions of the existence of graph
maps. We applied these complexes to prove the nonexistence of graph maps about
Kneser graphs. We prove that the fundamental groups of r-neighborhood complexes
are closely related to the (2r)-fundamental groups defined in the author's
previous paper.

14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics