  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.
