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APPROX
Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

Authors: Gary L. Miller, Noel J. Walkington, and Alex L. Wang

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)


Abstract
We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt.

Cite as

Gary L. Miller, Noel J. Walkington, and Alex L. Wang. Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{miller_et_al:LIPIcs.APPROX-RANDOM.2019.8,
  author =	{Miller, Gary L. and Walkington, Noel J. and Wang, Alex L.},
  title =	{{Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.8},
  URN =		{urn:nbn:de:0030-drops-112236},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.8},
  annote =	{Keywords: Hardy, Muckenhoupt, Laplacian, eigenvalue, effective resistance}
}
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