Thresholds and expectation thresholds

Jeff Kahn; Gil Kalai

doi:10.1017/S0963548307008474

Thresholds and expectation thresholds

Jeff Kahn, Gil Kalai

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article

24 Scopus citations

Abstract

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 p_c for that p for which the probability that G contains (a copy of) H is 1/2. Then (conjecture) p_c = O(P_E log n). Possible connections with discrete isoperimetry are also discussed.

Original language	English (US)
Pages (from-to)	495-502
Number of pages	8
Journal	Combinatorics Probability and Computing
Volume	16
Issue number	3
DOIs	https://doi.org/10.1017/S0963548307008474
State	Published - May 1 2007

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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Kahn, J., & Kalai, G. (2007). Thresholds and expectation thresholds. Combinatorics Probability and Computing, 16(3), 495-502. https://doi.org/10.1017/S0963548307008474

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