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Cheeger inequalities for unbounded graph Laplacians

Frank Bauer; Matthias Keller; Radosław K. Wojciechowski — 2015

Journal of the European Mathematical Society

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

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