The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is an extension of the tree-metric theorem to more general dissi
Reconstruction of rooted trees from subtrees
β Scribed by Meei Pyng Ng; Nicholas C. Wormald
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 888 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0166-218X
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A probably very difficult question of Nash-Williams asks whether any two hypomorphic trees are isomorphic. In the present paper, we consider rooted trees rather than trees and give an affirmative answer to the corresponding version of Nash-Williams' question, i.e., we show that any two hypomorphic r
## Abstract A necessary condition for the decomposition of a tree __T__ into subtrees, each isomorphic to a tree from a given set of trees is presented. We also present a characterization of the set of trees for which the condition is sufficient. Many examples are given.
First it is shown that for any rooted tree T with n vertices, and parameter m G n, there is a ''shortcutting'' set S of at most m arcs from the transitive closure Ε½ . T\* of T such for any Β¨, w g T \*, there is a dipath in T j S from Β¨to w of length Ε½ Ε½ .. Ε½ O β£ m, n . An equivalent result has been