English

2-Matching Complexes

Combinatorics 2021-02-01 v2 Algebraic Topology

Abstract

A 22-matching complex is a simplicial complex which captures the relationship between 22-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 22-matching complex transforms from a sphere to a point with the addition of leaves. We end the paper by defining kk-matching sequences and looking at the 11- and 22-matching complexes of wheel graphs and perfect caterpillar graphs.

Keywords

Cite

@article{arxiv.1909.10406,
  title  = {2-Matching Complexes},
  author = {Julianne Vega},
  journal= {arXiv preprint arXiv:1909.10406},
  year   = {2021}
}