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Counting rooted spanning forests in complete multipartite graphs

A 2004 Preprint by L. Székely

  • 2004:01
  • Jin and Liu discovered an elegant formula for the number of rooted spanning forests in the complete bipartite graph $K _ {a1,a2}$, with $b _ 1$ roots in the first vertex class and $b _ 2$ roots in the second vertex class. We give a simple proof to their formula, and a generalization for complete m-partite graphs, using the multivariate Lagrange inverse.

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