TY - JOUR
T1 - Phylogenetic trees defined by at most three characters
AU - Huber, Katharina T.
AU - Linz, Simone
AU - Moulton, Vincent
AU - Semple, Charles
N1 - 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.
PY - 2024/11/15
Y1 - 2024/11/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85210258752&partnerID=8YFLogxK
U2 - 10.37236/12560
DO - 10.37236/12560
M3 - Article
SN - 1077-8926
VL - 31
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 4
M1 - P4.42
ER -