TY  - JOUR
A1  - Keller, Matthias
A1  - Mugnolo, Delio
T1  - General Cheeger inequalities for p-Laplacians on graphs
JF  - Theoretical ecology
N2  - We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics. For the non-normalized case, our bounds on the spectral gap of p-Laplacians are already significantly better for finite graphs and for infinite graphs they yield non-trivial bounds even in the case of unbounded vertex degree. We, furthermore, give upper bounds by the Cheeger constant and by the exponential volume growth of distance balls. (C) 2016 Elsevier Ltd. All rights reserved.
KW  - Cheeger inequalities
KW  - Spectral theory of graphs
KW  - Intrinsic metrics for Dirichlet forms
Y1  - 2016
U6  - https://doi.org/10.1016/j.na.2016.07.011
SN  - 0362-546X
SN  - 1873-5215
VL  - 147
SP  - 80
EP  - 95
PB  - Elsevier
CY  - Oxford
ER  -