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Thresholds and Expectation Thresholds

Published online by Cambridge University Press:  01 May 2007

JEFF KAHN  and
GIL KALAI
JEFF KAHN
Affiliation:
Department of Mathematics, Rutgers University, Piscataway NJ 08854USAjkahn@math.rutgers.edu
GIL KALAI
Affiliation:
Department of Mathematics, The Hebrew University, Jerusalem, Israelkalai@math.huji.ac.il
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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 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.

Type
PROBLEM SECTION
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 3 , May 2007 , pp. 495 - 502
Copyright
Copyright © Cambridge University Press 2007

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