A reverse Aldous–Broder algorithm

The Aldous–Broder algorithm provides a way of sampling uniformly random spanning tree for finite connected graphs using simple walk. Namely, start walk on graph and stop at the cover time. formed by all first-entrance edges has law uniform tree. Here we show that last-exit also This answers question Tom Hayes Cris Moore from 2010. proof relies bijection is related to BEST theorem in theory. We give other applications our results, including new proofs reversibility loop-erased walk, itself, Wilson’s algorithm.