Generating Functions for Multi-labeled Trees

Czabarka, E, Erdős, P L, Johnson, V and Moulton, V ORCID: (2013) Generating Functions for Multi-labeled Trees. Discrete Applied Mathematics, 161 (1-2). pp. 107-117. ISSN 0166-218X

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Multi-labeled trees are a generalization of phylogenetic trees that are used, for example, in the study of gene versus species evolution and as the basis for phylogenetic network construction. Unlike phylogenetic trees, in a leaf-multi-labeled tree it is possible to label more than one leaf by the same element of the underlying label set. In this paper we derive formulae for generating functions of leaf-multi-labeled trees and use these to derive recursions for counting such trees. In particular, we prove results which generalize previous theorems by Harding on so-called tree-shapes, and by Otter on relating the number of rooted and unrooted phylogenetic trees.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Pure Connector
Date Deposited: 03 Feb 2014 11:18
Last Modified: 24 Oct 2022 06:02
DOI: 10.1016/j.dam.2012.08.010

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