Sharp Thresholds of Graph properties, and the k-sat Problem (1998)
| Venue: | J. Amer. Math. Soc |
| Citations: | 140 - 6 self |
BibTeX
@ARTICLE{Friedgut98sharpthresholds,
author = {Ehud Friedgut},
title = {Sharp Thresholds of Graph properties, and the k-sat Problem},
journal = {J. Amer. Math. Soc},
year = {1998},
volume = {12},
pages = {1017--1054}
}
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Abstract
Given a monotone graph property P , consider p (P ), the probability that a random graph with edge probability p will have P . The function d p (P )=dp is the key to understanding the threshold behavior of the property P . We show that if d p (P )=dp is small (corresponding to a non-sharp threshold), then there is a list of graphs of bounded size such that P can be approximated by the property of having one of the graphs as a subgraph. One striking consequences of this result is that a coarse threshold for a random graph property can only happen when the value of the critical edge probability is a rational power of n.
