Combinatorica
Perfect matchings in random s-uniform hypergraphs
Random Structures & Algorithms
Computing Graph Properties by Randomized Subcube Partitions
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Influences in Product Spaces: KKL and BKKKL Revisited
Combinatorics, Probability and Computing
Triangle Factors in Random Graphs
Combinatorics, Probability and Computing
Variable Influences in Conjunctive Normal Forms
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Are many small sets explicitly small?
Proceedings of the forty-second ACM symposium on Theory of computing
Almost isoperimetric subsets of the discrete cube
Combinatorics, Probability and Computing
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We consider relations between thresholds for monotone set properties and simple lower bounds for such thresholds. A motivating example (Conjecture 2): Given an n-vertex graph H, write pE for the least p such that, for each subgraph H' of H, the expected number of copies of H' in G=G(n, p) is at least 1, and pc for that p for which the probability that G contains (a copy of) H is 1/2. Then (conjecture) pc=O(pElog n). Possible connections with discrete isoperimetry are also discussed.