A multi-labeled tree is a rooted tree whose leaves carry positive integer labels, with repeated labels allowed. This distinguishes it from a leaf-labeled phylogenetic tree, whose tree leaf labels are normally distinct.
Multi-labeled trees arise by unfolding phylogenetic networks. Conversely, folding a multi-labeled tree identifies isomorphic rooted subtrees and may produce a phylogenetic network. Moulton and Spillner (2026) give labeling algorithms that extend the tree leaf labels to all vertices and characterize the resulting partitions of multisets. They also obtain a bijection between labelable phylogenetic networks and certain multiset partitions.
