Extremal problems related to Betti numbers of flag complexes

2011/09/22 by Michal Adamaszek, Adamaszek, Michal
Mathematics · #05E45 #55U10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E45 #msc:55U10

paper · pdf · doi:10.48550/arxiv.1109.4775

V4: rewritten, no new results

arxiv created 2013/04/17 · arxiv updated 2013/04/18

Abstract

We study the problem of maximizing Betti numbers of simplicial complexes. We prove an upper bound of 1.32ⁿ for the sum of Betti numbers of any n-vertex flag complex and 1.25ⁿ 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.

Related

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