Treelike quintet systems

Abstract

Let $X$ be a finite set. We give criterion to say if a system of trees $\mathcal{P}=\{T_i{\}}_i$ with leaf sets $L(T_i)\in \left(\genfrac{}{}{0ex}{}{X}{5}\right)$ 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 $T_i$.

12 pages