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Polynomial-time recovery of planted cliques below the square-root scale

TheoremDB P3130 · theoretical computer science

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

Problem statement

Fix δ>0\delta>0. Given a graph sampled by first drawing G(n,1/2)G(n,1/2) and then planting a uniformly random clique of size k=⌈n1/2−δ⌉k=\lceil n^{1/2-\delta}\rceil, is there a randomized polynomial-time algorithm that recovers the planted vertex set with probability tending to one?

Lean 4

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

References
  1. [1]TheoremDB P3130 link

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