A Cheeger-Type Inequality on Simplicial Complexes
Combinatorics
2012-10-29 v3 Computational Geometry
Abstract
In this paper, we consider a variation on Cheeger numbers related to the coboundary expanders recently defined by Dotterer and Kahle. A Cheeger-type inequality is proved, which is similar to a result on graphs due to Fan Chung. This inequality is then used to study the relationship between coboundary expanders on simplicial complexes and their corresponding eigenvalues, complementing and extending results found by Gundert and Wagner. In particular, we find these coboundary expanders do not satisfy natural Buser or Cheeger inequalities.
Cite
@article{arxiv.1209.5091,
title = {A Cheeger-Type Inequality on Simplicial Complexes},
author = {John Steenbergen and Caroline Klivans and Sayan Mukherjee},
journal= {arXiv preprint arXiv:1209.5091},
year = {2012}
}