A characterization of two-dimensional Buchsbaum matching complexes

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....

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Bibliographic Details
Main Authors: Goeckner, Bennet, Herr, Fran, JonesII, Legrand, Rowlands, Rowan
Format: Journal Article
Language:English
Published: 21-10-2021
Subjects:
Mathematics - Combinatorics
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.
DOI:10.48550/arxiv.2110.11302