Tight bounds on vertex connectivity under sampling

Keren Censor-Hillel, Mohsen Ghaffari, George Giakkoupis, Bernhard Haeupler, Fabian Kuhn

Research output: Contribution to journalArticlepeer-review


A fundamental result by Karger [10] states that for any λ-edge-connected graph with n nodes, independently sampling each edge with probability p = Ω(log(n)/λ) results in a graph that has edge connectivity Ω(λp), with high probability. This article proves the analogous result for vertex connectivity, when either vertices or edges are sampled. We show that for any k-vertex-connected graph G with n nodes, if each node is independently sampled with probability p = Ω(√log(n)/k), then the subgraph induced by the sampled nodes has vertex connectivity Ω(kp2), with high probability. If edges are sampled with probability p = Ω(log(n)/k), then the sampled subgraph has vertex connectivity Ω(kp), with high probability. Both bounds are existentially optimal.

Original languageEnglish
Article number19
JournalACM Transactions on Algorithms
Issue number2
StatePublished - May 2017


  • Graph sampling
  • Vertex connectivity

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


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