Extremal problems related to Betti numbers of flag complexes
Combinatorics
2013-04-18 v4
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.
Keywords
Cite
@article{arxiv.1109.4775,
title = {Extremal problems related to Betti numbers of flag complexes},
author = {Michal Adamaszek},
journal= {arXiv preprint arXiv:1109.4775},
year = {2013}
}
Comments
V4: rewritten, no new results