# Gorenstein and Cohen-Macaulay Matching Complexes

@article{Nikseresht2021GorensteinAC, title={Gorenstein and Cohen-Macaulay Matching Complexes}, author={Ashkan Nikseresht}, journal={Journal of Algebra and Its Applications}, year={2021} }

Let H be a simple undirected graph. The family of all matchings of H forms a simplicial complex called the matching complex of H. Here , we give a classification of all graphs with a Gorenstein matching complex. Also we study when the matching complex of H is CohenMacaulay and, in certain classes of graphs, we fully characterize those graphs which have a Cohen-Macaulay matching complex. In particular, we characterize when the matching complex of a graph with girth at least 5 or a complete graph…

## 2 Citations

### A characterization of two-dimensional Buchsbaum matching complexes

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- 2021

. 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…

### Perfect Matching Complexes of Honeycomb Graphs

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- 2022

The perfect matching complex of a graph is the simplicial complex on the edge set of the graph with facets corresponding to perfect matchings of the graph. This paper studies the perfect matching…

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