A Characterization of Two-Dimensional Buchsbaum Matching Complexes

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 i...

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Bibliographic Details
Published in:	The Electronic journal of combinatorics Vol. 30; no. 1
Main Authors:	Goeckner, Bennet, Herr, Fran, Jones, Legrand, Rowlands, Rowan
Format:	Journal Article
Language:	English
Published:	24-02-2023
Online Access:	Get full text
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Summary:	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.
ISSN:	1077-8926 1077-8926
DOI:	10.37236/11196