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.
PACM Colloquium: Counting Connected Graphs
Joel Spencer, New York University
Oct 24 2016 - 4:00pm
214 Fine Hall