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SIAM J. Discrete Math. 26, pp. 89-101 (13 pages)
Cohen–Macaulay Graphs and Face Vectors of Flag Complexes
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Add to FacebookWe 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 $h$-vectors 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.
© 2012 Society for Industrial and Applied Mathematics
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Received December 14, 2010
Accepted November 18, 2011
Published online February 09, 2012
Accepted November 18, 2011
Published online February 09, 2012
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