2019/09/23 by Vega, Julianne
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.10406
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.