Identifying phylogenetic trees Original Research Article

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection image of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays image have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when image identifies an X-tree, and the second describes when a compatible subset of image is of maximum size.