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On the Expansion of the Giant Component in Percolated (n, d,λ) Graphs

Published online by Cambridge University Press:  01 May 2007

ERAN OFEK
Affiliation:
Department of Computer Science and Applied Mathematics, Weizmann Institute, Rehovot 76100, Israel (e-mail: eran.ofek@weizmann.ac.il)
Corresponding
E-mail address:

Abstract

Let dd0 be a sufficiently large constant. An graph G is a d-regular graph over n vertices whose second-largest (in absolute value) eigenvalue is at most . For any 0<p<1, Gp is the graph induced by retaining each edge of G with probability p. It is known that for the graph Gp almost surely contains a unique giant component (a connected component with linear number vertices). We show that for the giant component of Gp almost surely has an edge expansion of at least .

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Copyright © Cambridge University Press 2006

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