Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matching complexes of trees and applications of the matching tree
  algorithm   A matching complex of a simple graph $G$ is a simplicial complex with faces
given by the matchings of $G$. The topology of matching complexes is
mysterious; there are few graphs for which the homotopy type is known. Marietti
and Testa showed that matching complexes of forests are contractible or
homotopy equivalent to a wedge of spheres. We study two specific families of
trees. For caterpillar graphs, we give explicit formulas for the number of
spheres in each dimension and for perfect binary trees we find a strict
connectivity bound. We also use a tool from discrete Morse theory called the
\textit{Matching Tree Algorithm} to study the connectivity of honeycomb graphs,
partially answering a question raised by Jonsson.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn