Abstract
We describe a technique for determining the thresholds for the appearance of cores in random structures. We use it to determine (i) the threshold for the pure literal rule to find a satisfying assignment for a random instance of r-SAT, r ≥ 3, and (ii) the threshold for the appearance of a k-core in a random r-uniform hypergraph for all r, k ≥ 2, r + k > 4.
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