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A Sharp Threshold for Network Reliability

  • MICHAEL KRIVELEVICH (a1), BENNY SUDAKOV (a2) and VAN H. VU (a3)

Abstract

Given a graph G on n vertices with average degree d, form a random subgraph Gp by choosing each edge of G independently with probability p. Strengthening a classical result of Margulis we prove that, if the edge connectivity k(G) satisfies k(G) [Gt ] d/log n, then the connectivity threshold in Gp is sharp. This result is asymptotically tight.

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A Sharp Threshold for Network Reliability

  • MICHAEL KRIVELEVICH (a1), BENNY SUDAKOV (a2) and VAN H. VU (a3)

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