2-Matching Complexes
Combinatorics
2021-02-01 v2 Algebraic Topology
Abstract
A -matching complex is a simplicial complex which captures the relationship between -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 -matching complex transforms from a sphere to a point with the addition of leaves. We end the paper by defining -matching sequences and looking at the - and -matching complexes of wheel graphs and perfect caterpillar graphs.
Cite
@article{arxiv.1909.10406,
title = {2-Matching Complexes},
author = {Julianne Vega},
journal= {arXiv preprint arXiv:1909.10406},
year = {2021}
}