A characterization of two-dimensional Buchsbaum matching complexes

Bennet Goeckner; Fran Herr; Legrand Jones; Rowan Rowlands

A characterization of two-dimensional Buchsbaum matching complexes

Combinatorics 2023-01-20 v3

Authors: Bennet Goeckner , Fran Herr , Legrand Jones , Rowan Rowlands

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.

Keywords

graph theory cohomology simplicial complexes

Cite

@article{arxiv.2110.11302,
  title  = {A characterization of two-dimensional Buchsbaum matching complexes},
  author = {Bennet Goeckner and Fran Herr and Legrand Jones and Rowan Rowlands},
  journal= {arXiv preprint arXiv:2110.11302},
  year   = {2023}
}

Comments

Some 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

A characterization of two-dimensional Buchsbaum matching complexes

Abstract

Keywords

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