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EXPANSION CONSTANTS AND HYPERBOLIC EMBEDDINGS OF FINITE GRAPHS

Part of: Discrete mathematics in relation to computer science Graph theory Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  19 November 2014

Tae Hattori  and
Atsushi Kasue
Tae Hattori
Affiliation:
Ishikawa National College of Technology, Tsubata Kahoku-gun, Ishikawa, 920-0329, Japan email [email protected]
Atsushi Kasue
Affiliation:
Department of Mathematics, Kanazawa University, Kanazawa, Ishikawa, 920-1192, Japan email [email protected]
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Abstract

In this paper, we study a finite connected graph which admits a quasi-monomorphism to hyperbolic spaces and give a geometric bound for the Cheeger constants in terms of the volume, an upper bound of the degree, and the quasi-monomorphism.

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 68R10: Graph theory (including graph drawing)
Type
Research Article
Information
Mathematika , Volume 61 , Issue 1 , January 2015 , pp. 1 - 13
Copyright
Copyright © University College London 2014 

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