Geodesic
A characterization of two-dimensional Buchsbaum matching complexes
Bennet Goeckner1 ; Fran Herr2 ; Legrand Jones3 ; Rowan Rowlands2
1University of San Diego
2University of Washington
3Indiana University
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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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 : 10.37236/11196
Classification : 05C70, 13F55, 05E45
Mots-clés : simplicial complex, two-dimensional Buchsbaum complexes

Bennet Goeckner  1   ; Fran Herr  2   ; Legrand Jones  3   ; Rowan Rowlands  2

1 University of San Diego
2 University of Washington
3 Indiana University 
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     title = {A characterization of two-dimensional {Buchsbaum} matching complexes},
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Bennet Goeckner; Fran Herr; Legrand Jones; Rowan Rowlands. A characterization of two-dimensional Buchsbaum matching complexes. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11196

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