The Emergence of a Giant Component in Random Subgraphs of Pseudo-Random Graphs

Alan Frieze, Michael Krivelevich, Ryan Martin

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a d-regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ. which is second largest in absolute value satisfies λ = o(d). Let G p with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of G p is O(log n) and if α > 1. then G p contains a unique giant component of size Ω(n), with all other components of size O(log n).

Original languageEnglish
Pages (from-to)42-50
Number of pages9
JournalRandom Structures and Algorithms
Volume24
Issue number1
DOIs
StatePublished - Jan 2004

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