Cohen-macaulay graphs and face vectors of flag complexes

David Cook, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We introduce a construction on a flag complex that by means of modifying the associated graph generates a new flag complex whose h-vector is the face vector of the original complex. This construction yields a vertex-decomposable, hence Cohen-Macaulay, complex. From this we get a (nonnumerical) characterization of the face vectors of flag complexes and deduce also that the face vector of a flag complex is the h-vector of some vertex-decomposable flag complex. We conjecture that the converse of the latter is true and prove this, by means of an explicit construction, for hvectors of Cohen-Macaulay flag complexes arising from bipartite graphs. We also give several new characterizations of bipartite graphs with Cohen-Macaulay or Buchsbaum independence complexes.

Original languageEnglish
Pages (from-to)89-101
Number of pages13
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2012


  • Cohen-Macaulay
  • Face vector
  • H-vector
  • Independence complex
  • Stanley-Reisner ideal
  • Vertex-decomposable

ASJC Scopus subject areas

  • Mathematics (all)


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