Let C(n,k) be the number of labelled connected graphs with n vertices and n-1+k edges. For k=0 (trees) we have Cayley's Formula. We examine the asymptotics of C(n,k). There are several approaches involving supercritical dominant components in random graphs, local limit laws, Brownian excursions, Parking functions and other topics.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
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