Summary
Last time we saw a number of properties of graphs, such as connectivity, where the probability that an Erdős–Rényi random graph $ G(n,p)$ satisfies the property is asymptotically either zero or one. And this zero or one depends on whether the parameter $ p$ is above or below a universal threshold (that depends only on $ n$ and the property in question). To remind the reader, the Erdős–Rényi random “graph” $ G(n,p)$ is a distribution over graphs that you draw from by including each edge independe...