Maximal Betti number of a flag simplicial complex

Details Maximal Betti number of a flag simplicial complex Maximal Betti number of a flag simplicial complex

2011-09-22

arxiv.org/abs/1109.4775v2

Mathematics

Combinatorics

Short note. If this is a known result, any reference will be appreciated. V2: added references and a conjecture on bipartite g

Scientific paper

We prove that the homology of a flag simplicial complex with n vertices has dimension at most 4^(n/5), which is approximately 1.32^n. The same upper bound holds for the Euler characteristic and therefore, in more combinatorial language, for the alternating number of independent sets in any n-vertex graph. All bounds are asymptotically tight. We also study the same question for the independence complexes of bipartite graphs.

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