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Putting together .[Thm]Take a random graph G(N,p)with w(log4NN)≤p≤1-2(1). Its adjacency matrix,as a bi-variate function f, has the following w.p.1-0(1) Q(⑤=2(log(pN). ·[Thm]Forp=o(N-67),TD(⑤=O(1)w.h.p. 、[Thm]For p=N-(0,PT(⑤=O(1)w.h.p. Taking p between w(log4N/N)and o(N-6/7)gives the separationPutting together • [Thm] Take a random graph G(N,p) with ω(log4N/N) ≤ p ≤ 1-Ω(1). Its adjacency matrix, as a bi-variate function f, has the following w.p. 1-o(1) Q(f) = Ω(log(pN)). • [Thm] For p = o(N-6/7), TD(f) = O(1) w.h.p. • [Thm] For p = N-Ω(1) , PT(f) = O(1) w.h.p. • Taking p between ω(log4N/N) and o(N-6/7) gives the separation
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