The average number of spanning trees in sparse graphs with given degrees. (June 2017) - Greenhill, Catherine; Isaev, Mikhail; Kwan, Matthew; McKay, Brendan D.
Abstract: We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence d = ( d 1, …, d n ), provided that the number of edges is at least n + 1 2 d max 4, where d max is the maximum degree. A key part of our argument involves establishing a concentration result for a certain family of functions over random trees with given degrees, using Prüfer codes.