Non-binary universal tree-based networks

A tree-based network N on X is called universal if every phylogenetic tree on X is a base tree for N. Recently, binary universal tree-based networks have attracted great attention in the literature and their existence has been analyzed in various studies. In this note, we extend the analysis to non-binary networks and show that there exist both a rooted and an unrooted non-binary universal tree-based network with n leaves for all positive integers n.