A Sharp Threshold for Network Reliability

Authors:
Michael Krivelevich;Benny Sudakov;Van H. Vu
Affiliations:
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: krivelev@math.tau.ac.il);Department of Mathematics, Princeton University, Princeton, NJ 08540, USA and Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail: bsudakov@math.princeton.edu);Theory Group, Microsoft Research, Redmond, WA 98052, USA (e-mail: vanvu@ucsd.edu/ Web: http:////www.math.ucsd.edu//&tilde/vanvu)
Venue:
Combinatorics, Probability and Computing
Year:
2002

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Abstract

Given a graph G on n vertices with average degreed, form a random subgraph Gp bychoosing each edge of G independently with probabilityp. Strengthening a classical result of Margulis we provethat, if the edge connectivity k(G) satisfiesk(G) d/log n, then theconnectivity threshold in Gp is sharp.This result is asymptotically tight.