22
Threshold Functions for
Subgraphs
•
[Erdos and Reny]
•
Edge probability Pr(t) = p(n) = some function
•
•
Main theorem of random graphs
:
For any monotone property C there exists a
threshold function t(n) s.t.
–
If p(n)
¿
t(n) then lim
n
Pr(C) = 0
–
If p(n)
À
t(n) then lim
n
Pr(C) = 1