Phylogenetic trees defined by at most three characters

Huber, Katharina T., Linz, Simone, Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Semple, Charles (2024) Phylogenetic trees defined by at most three characters. Electronic Journal of Combinatorics, 31 (4). ISSN 1077-8926

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Abstract

In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular sequences or morphological data. Interestingly, it has been known for some time that any binary phylogenetic tree can be (convexly) defined by a set of at most four characters, and that there are binary phylogenetic trees for which three characters are not enough. Thus, it is of interest to characterise those phylogenetic trees that are defined by a set of at most three characters. In this paper, we provide such a characterisation, in particular proving that a binary phylogenetic tree T is defined by a set of at most three characters precisely if T has no internal subtree isomorphic to a certain tree.

Item Type:	Article
Additional Information:	Acknowledgements: KTH and VM would like to thank The Royal Society in the context of its International Exchanges Scheme for support and also the University of Canterbury for hosting them during a brief visit. SL and CS were supported by the New Zealand Marsden Fund. All authors would like to thank the Institute for Mathematical Sciences, National University of Singapore where some of the research was partially completed while they were visiting in 2023. Lastly, we thank the anonymous referees for highlighting and oversight in the proof of Lemma 8 and providing a reference for resolving it and, more generally, for their close reading of the paper and comments.
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Computational Biology Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	22 Oct 2024 12:30
Last Modified:	10 Dec 2024 01:45
URI:	https://ueaeprints.uea.ac.uk/id/eprint/97106
DOI:	10.37236/12560

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