Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long cycles in locally expanding graphs, with applications   We provide sufficient conditions for the existence of long cycles in locally
expanding graphs, and present applications of our conditions and techniques to
Ramsey theory, random graphs and positional games.

6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga