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Random trial determines thresholds for cores in hypergraphs and Boolean formulas, suggesting new insights into structural properties.
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 appearance of a k ‐core in a random r ‐uniform hypergraph for all r, k ≥ 2, r + k > 4, and (ii) the threshold for the pure literal rule to find a satisfying assignment for a random instance of r ‐SAT, r ≥ 3.
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Michael Molloy (2005) studied this question.
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