Minimum triplet covers of binary phylogenetic X-trees.
J Math Biol
; 75(6-7): 1827-1840, 2017 12.
Article
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| MEDLINE
| ID: mdl-28608005
ABSTRACT
Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed from the distances between the leaves (when the edges are given any strictly positive lengths). Moreover, a linear number of these pairwise distance values suffices to determine both the tree and its edge lengths. A natural set of pairs of leaves is provided by any 'triplet cover' of the tree (based on the fact that each non-leaf vertex is the median vertex of three leaves). In this paper we describe a number of new results concerning triplet covers of minimum size. In particular, we characterize such covers in terms of an associated graph being a 2-tree. Also, we show that minimum triplet covers are 'shellable' and thereby provide a set of pairs for which the inter-leaf distance values will uniquely determine the underlying tree and its associated branch lengths.
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MEDLINE
Asunto principal:
Filogenia
/
Modelos Genéticos
Idioma:
En
Año:
2017
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Article