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Eigenvalue ratios of non-negatively curved graphs

Liu, Shiping; Peyerimhoff, Norbert

Eigenvalue ratios of non-negatively curved graphs Thumbnail


Shiping Liu


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.


Liu, S., & Peyerimhoff, N. (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, Probability and Computing, 27(5), 829-850.

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


Accepted Journal Article (398 Kb)

Copyright Statement
This article has been published in a revised form in Combinatorics, probability and computing 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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