TY - JOUR
T1 - Thresholds and expectation thresholds
AU - Kahn, Jeff
AU - Kalai, Gil
PY - 2007/5
Y1 - 2007/5
N2 - 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(PE log n). Possible connections with discrete isoperimetry are also discussed.
AB - 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(PE log n). Possible connections with discrete isoperimetry are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=34247640604&partnerID=8YFLogxK
U2 - 10.1017/S0963548307008474
DO - 10.1017/S0963548307008474
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AN - SCOPUS:34247640604
SN - 0963-5483
VL - 16
SP - 495
EP - 502
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 3
ER -