Greenhill, Catherine; Isaev, Mikhail; Kwan, Matthew; McKay, Brendan D.
We give an asymptotic expression for the expected number of
spanning trees in a random graph with a given degree sequence
d = (d₁, . . . , dn), provided that the number of edges is at least
n + 1/2d⁴max, where dmax 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
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