#####
Séminaire Lotharingien de Combinatoire, B76a (2016), 14 pp.

# Simone Calamai and Elena Rubei

# Treelike Quintet Systems

**Abstract.**
We give a criterion to say if
a system of trees **P** = {*T*_{i}}_{i}
with leaf sets *L*(*T*_{i}) in the 5-subsets of
*X*
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}.

Received: June 24, 2016.
Revised: October 2, 2016.
Accepted: October 3, 2016.

The following versions are available: