Gorenstein and Cohen-Macaulay Matching Complexes

  title={Gorenstein and Cohen-Macaulay Matching Complexes},
  author={Ashkan Nikseresht},
  journal={Journal of Algebra and Its Applications},
  • 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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