Flag complexes can be replaced by balanced complexes with the same f-vector and no smaller top Betti number, yielding new upper and lower bounds on face numbers in terms of homology.
An extended Euler-Poinca r´ e theorem.Acta Math
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Flag complexes and homology
Flag complexes can be replaced by balanced complexes with the same f-vector and no smaller top Betti number, yielding new upper and lower bounds on face numbers in terms of homology.