Thresholds and expectation thresholds
Combinatorics
2007-05-23 v2 Probability
Abstract
Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies of H' in G is at least 1/2 for every subgraph H' of H. Let p be the value for which the probability that G contains a copy of H is 1/2. Conjecture: p/q = O(log n). Related conjectures for general Boolean functions, and a possible connection with discrete isoperimetry are discussed.
Keywords
Cite
@article{arxiv.math/0603218,
title = {Thresholds and expectation thresholds},
author = {Jeff Kahn and Gil Kalai},
journal= {arXiv preprint arXiv:math/0603218},
year = {2007}
}
Comments
The gap between expectations and reality is studied, 7 pages