Glossary

A split is the division of a collection of taxa into disjoint sets $S$ and $S^{\textrm{c}}$, which is represented as $S \mid S^{\textrm{c}}$. Note that the removal of any edge of the tree will produce two smaller trees, so that if taxa are assigned to the leaves of a tree, the edge's removal will naturally divide the taxa into two disjoint sets, thus forming a split.

Thus, we can represent any edge of a phylogeny with the split to which it corresponds. Conversely, a character also corresponds to a split, as it divides all possible taxa into two disjoint sets. Thus, a common phylogenetic problem is to use the notion of split to construct a phylogeny given a collection of characters, often encoded by a character table.