Trees and Matchings

@article{Kenyon2000TreesAM,
  title={Trees and Matchings},
  author={Richard W. Kenyon and James Gary Propp and David Bruce Wilson},
  journal={Electron. J. Comb.},
  year={2000},
  volume={7}
}
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. We show that the weighted, directed spanning trees (often called arborescences) of any planar graph $G$ can be put into a one-to-one weight… Expand
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