X-Trees and Weighted Quartet Systems

@article{Dress2003XTreesAW,
  title={X-Trees and Weighted Quartet Systems},
  author={Andreas W. M. Dress and P{\'e}ter L. Erd{\"o}s},
  journal={Annals of Combinatorics},
  year={2003},
  volume={7},
  pages={155-169}
}
Abstract.In this note, we consider a finite set X and maps W from the set $ \mathcal{S}_{2|2} (X) $ of all 2, 2- splits of X into $ \mathbb{R}_{\geq 0} $. We show that such a map W is induced, in a canonical way, by a binary X-tree for which a positive length $ \mathcal{l} (e) $ is associated to every inner edge e if and only if (i) exactly two of the three numbers W(ab|cd),W(ac|bd), and W(ad|cb) vanish, for any four distinct elements a, b, c, d in X, (ii) $ a \neq d \quad\mathrm{and}\quad… CONTINUE READING

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