Abstract
Evolutionary trees of biology are represented by a special class of labelled trees, termed phylogenetic trees. These are characterised by having disjoint subsets of the labelling set assigned to the points of a tree, in such a way that no point of degree less than 3 is assigned an empty set of labels. By a binary tree is meant one in which every point has degree 1 or 3. The exact and asymptotic numbers of binary phylogenetic trees are determined under the presence or absence of two additional conditions on the labelling. The optional constraints studied require nonempty label sets to be singletons, and that only endpoints be labelled.
The second author is grateful for the support of the Australian Research Grants Committee for the project “Numerical Implementation of Unlabelled Graph Counting Algorithms”, under which research and computing for this paper were performed.
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© 1981 Springer-Verlag
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Foulds, L.R., Robinson, R.W. (1981). Enumeration of binary phylogenetic trees. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091819
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DOI: https://doi.org/10.1007/BFb0091819
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