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2007 The Spectral Gap of a Random Subgraph of a Graph
Fan Chung, Paul Horn
Internet Math. 4(2-3): 225-244 (2007).

Abstract

We examine the relationship of a graph $G$ and its random subgraphs, which are defined by independently choosing each edge with probability $p$. Suppose that $G$ has a spectral gap $\lambda$ (in terms of its normalized Laplacian) and minimum degree $d_{\min}$. Then we can show that a random subgraph of $G$ on $n$ vertices with edge-selection probability $p$ almost surely has as its spectral gap $\lambda - O\big(\sqrt{\frac{\log n }{pd_{\min}}}+\frac{(\log n)^{3/2}}{pd_{\min}(\log \log n)^{3/2}}\big)$.

Citation

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Fan Chung. Paul Horn. "The Spectral Gap of a Random Subgraph of a Graph." Internet Math. 4 (2-3) 225 - 244, 2007.

Information

Published: 2007
First available in Project Euclid: 27 May 2009

zbMATH: 1206.68229
MathSciNet: MR2522877

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.4 • No. 2-3 • 2007
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