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Eigenvalue ratios of non-negatively curved graphs.

Liu, Shiping and Peyerimhoff, Norbert (2018) 'Eigenvalue ratios of non-negatively curved graphs.', Combinatorics, probability and computing., 27 (5). pp. 829-850.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/s0963548318000214
Publisher 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.
Date accepted:06 March 2018
Date deposited:01 May 2018
Date of first online publication:23 May 2018
Date first made open access:23 November 2018

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