Planted Subgraph Problems

Hiding a clique, an independent set or another subgraph in a random graph, and the hardness of finding or distinguishing it.

Status Statement Tags
Planted-Subgraph Character Sum
The source derives the formula governing low-degree detection of a planted subgraph, observes the character sum in it should be small for most graphs, and says it leaves the rigorous study of the question to future work. No bound is proved and none is stated as a target. 5 open
Average Case HardnessPlanted Subgraph Problemslower-boundadaptation (ai)
Sub-log Share Size for 2-out-of-n
The information-theoretic share size is exactly log n and Shamir’s scheme matches it. The source proves a (1/5) log log n lower bound for the computational setting with public information, leaving a log n versus log log n gap, and proves that beating log n by any constant factor is equivalent to a concrete planted clique-and-independent-set problem. 4 open
Average Case HardnessPlanted Subgraph ProblemsThreshold Secret Sharingtight-bound
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