Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-Matching Complexes   A $2$-matching complex is a simplicial complex which captures the
relationship between $2$-matchings of a graph. In this paper, we will use
discrete Morse Theory and the Matching Tree Algorithm to prove homotopical
results. We will consider a class of graphs for which the homotopy type of the
$2$-matching complex transforms from a sphere to a point with the addition of
leaves. We end the paper by defining $k$-matching sequences and looking at the
$1$- and $2$-matching complexes of wheel graphs and perfect caterpillar graphs.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con