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(1) When p=d/n for some constant d, the number of triangles in G(n,p) is independent of n.
(1) When p=d/n for some constant d, the number of triangles in G(n,p) is independent of n.
(2) The property that G(n,p) has diameter two has a sharp threshold at p = \sqrt(\dfrac{2\ln n}{n}).
(2) The property that G(n,p) has diameter two has a sharp threshold at p = \sqrt(\dfrac{2\ln n}{n}).
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(3) The disappearance if isolated vertices in G(n,p) has a sharp threshold at p = \dfrac{\ln n}{n}.
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(3) The disappearance of isolated vertices in G(n,p) has a sharp threshold at p = \dfrac{\ln n}{n}.
(4) When p=d/n, d > 1, there is a giant component consisting of a constant fraction of the vertices.
(4) When p=d/n, d > 1, there is a giant component consisting of a constant fraction of the vertices.
I will be covering material from the following book: http://www.cs.cornell.edu/jeh/book11April2014.pdf
I will be covering material from the following book: http://www.cs.cornell.edu/jeh/book11April2014.pdf