2021/10/21 by Goeckner, Bennet, Herr, Fran, Jones, Legrand +1
#05C70 #05E45 #13F55 #13H10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.11302
The matching complex M(G) of a graph G is the set of all matchings in G. A Buchsbaum simplicial complex is a generalization of both a homology manifold and a Cohen--Macaulay complex. We give a complete characterization of the graphs G for which M(G) is a two-dimensional Buchsbaum complex. As an intermediate step, we determine which graphs have matching complexes that are themselves connected graphs.