Extremal problems related to Betti numbers of flag complexes

Abstract

We study the problem of maximizing Betti numbers of simplicial complexes. We prove an upper bound of 1.32^n for the sum of Betti numbers of any n-vertex flag complex and 1.25^n for the independence complex of a triangle-free graph. These findings imply upper bounds for the Betti numbers of various related classes of spaces, including the neighbourhood complex of a graph. We also make some related observations.

V4: rewritten, no new results

References in corpus (3)

• Charge frustration and quantum criticality for strongly correlated fermions
• Combinatorial Alexander Duality -- a Short and Elementary Proof
• The independence polynomial of a graph at -1