Treelike quintet systems

TL;DR

This paper provides criteria to determine when a collection of 5-leaf trees can be combined into a single supertree that encompasses all leaves, aiding in the reconstruction of larger phylogenetic trees.

Contribution

It introduces a novel criterion for amalgamating a system of trees with 5-leaf subsets into a comprehensive supertree.

Findings

Established necessary and sufficient conditions for tree amalgamation.

Provided a method to verify if a system of trees can form a supertree.

Enhanced understanding of tree reconstruction from partial data.

Abstract

Let $X$ be a finite set. We give criterion to say if a system of trees ${\cal P}=\{T_i\}_i$ with leaf sets $L(T_i) \in {X \choose 5}$ can be amalgamated into a supertree, that is, if there exists a tree $T$ with $L(T)=X$ such that $T$ restricted to $ L(T_i)$ is equal to $T_i$.