Gorenstein and Cohen-Macaulay Matching Complexes

@article{Nikseresht2022GorensteinAC,
  title={Gorenstein and Cohen-Macaulay Matching Complexes},
  author={Ashkan Nikseresht},
  journal={Journal of Algebra and Its Applications},
  year={2022}
}
  • A. Nikseresht
  • Published 26 June 2021
  • Mathematics
  • Journal of Algebra and Its Applications
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… 

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References

SHOWING 1-10 OF 24 REFERENCES

Topology of matching, chessboard, and general bounded degree graph complexes

Abstract.We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a

A characterization of triangle-free Gorenstein graphs and Cohen–Macaulayness of second powers of edge ideals

We graph-theoretically characterize triangle-free Gorenstein graphs G. As an application, we classify when $$I(G)^2$$I(G)2 is Cohen–Macaulay.

Vertex decomposable graphs and obstructions to shellability

  • Russ Woodroofe
  • Mathematics
    Proceedings of the American Mathematical Society
  • 2009
Inspired by several recent papers on the edge ideal of a graph G, we study the equivalent notion of the independence complex of G. Using the tool of vertex decomposability from geometric

Chordal and Sequentially Cohen-Macaulay Clutters

The independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution.

MANIFOLD MATCHING COMPLEXES

The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we completely characterize the

Some Combinatorial Characterizations of Gorenstein Graphs with Independence Number Less Than Four

Let $$\alpha =\alpha (G)$$ be the independence number of a simple graph G with n vertices and I(G) be its edge ideal in $$S=K[x_1,\ldots , x_n]$$ . If S/I(G) is Gorenstein, the graph G is called

A note on equimatchable graphs

This paper characterize the equimatchable graphs of girth at least five and determine those graphs ofgirth five or more in which every minimal set of edges dominating edges is a minimum.

Cohen-Macaulay edge ideal whose height is half of the number of vertices

Abstract We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number #V(G) of the vertices. We give Cohen-Macaulay criteria for such graphs.

Exact sequences for the homology of the matching complex

The graphs with maximum induced matching and maximum matching the same size