Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, April 14, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matthew Kwan

Counting spanning trees in random regular graphs

The number of spanning trees in a graph is an important parameter in a surprising range of contexts. Particular attention has been given to regular graphs. We obtain a sharp asymptotic formula for the expected number of spanning trees in a random d-regular graph on n vertices, d = o(n^{1/3}). I will very briefly outline the proof, and then focus on an interesting component of the proof: analysis of a martingale based on the Prüfer code to establish concentration of a certain function over random trees. Joint work with Catherine Greenhill, Mikhail Isaev and Brendan McKay.

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