Shiping Liu
Eigenvalue ratios of non-negatively curved graphs
Liu, Shiping; Peyerimhoff, Norbert
Abstract
We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality CD(0, ∞). This estimate is independent of the size of the graph and provides a general method to obtain higher-order spectral estimates. The operation of taking Cartesian products is shown to be an efficient way for constructing new weighted graphs satisfying CD(0, ∞). We also discuss a higher-order Cheeger constant-ratio estimate and related topics about expanders.
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 6, 2018 |
Online Publication Date | May 23, 2018 |
Publication Date | Sep 30, 2018 |
Deposit Date | May 1, 2018 |
Publicly Available Date | Nov 23, 2018 |
Journal | Combinatorics, Probability and Computing |
Print ISSN | 0963-5483 |
Electronic ISSN | 1469-2163 |
Publisher | Cambridge University Press |
Peer Reviewed | Peer Reviewed |
Volume | 27 |
Issue | 5 |
Pages | 829-850 |
DOI | https://doi.org/10.1017/s0963548318000214 |
Public URL | https://durham-repository.worktribe.com/output/1332134 |
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Copyright Statement
This article has been published in a revised form in Combinatorics, probability and computing https://doi.org/10.1017/s0963548318000214. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2018.
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