A characterization of two-dimensional Buchsbaum matching complexes

Abstract

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.

arXiv commentSome material in Sections 3 and 4 have reordered to emphasize the main result of each section. Other small changes throughout based on referee feedback. To appear in the Electronic Journal of Combinatorics