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

Authors:
ERAN OFEK
Affiliations:
Department of Computer Science and Applied Mathematics, Weizmann Institute, Rehovot 76100, Israel (e-mail: eran.ofek@weizmann.ac.il)
Venue:
Combinatorics, Probability and Computing
Year:
2007

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Abstract

Let d e d0 be a sufficiently largeconstant. An (n, d, c √d) graph G is ad-regular graph over n vertices whose second-largest(in absolute value) eigenvalue is at most c√d. For any0pGp is the graph induced byretaining each edge of G with probability p. It isknown that for p 1/d the graphGp almost surely contains a unique giantcomponent (a connected component with linear number vertices). Weshow that for p ≥ 5c/√d the giant componentof Gp almost surely has an edge expansion of atleast 1/logn.