NDLI: CohenMacaulay Graphs and Face Vectors of Flag Complexes

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Nagel, Uwe Cook, David
Copyright Year	2012
Abstract	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 CohenMacaulay, 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 CohenMacaulay flag complexes arising from bipartite graphs. We also give several new characterizations of bipartite graphs with CohenMacaulay or Buchsbaum independence complexes.
Starting Page	89
Ending Page	101
Page Count	13
File Format	PDF
ISSN	08954801
DOI	10.1137/100818170
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	26
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-02-09
Access Restriction	Subscribed
Subject Keyword	Graphs and abstract algebra h-vector face vector CohenMacaulay Combinatorial aspects of simplicial complexes vertex-decomposable Special types StanleyReisner ideal Stanley-Reisner face rings; simplicial complexes independence complex
Content Type	Text
Resource Type	Article
Subject	Mathematics

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CohenMacaulay Graphs and Face Vectors of Flag Complexes