Journal of Graph Algorithms and Applications

Non-binary universal tree-based networks

Mareike Fischer, Michelle Galla, and Kristina Wicke

Vol. 26, no. 1, pp. 81-90, 2022. Regular paper.

Abstract 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 $n$.

Keywords: phylogenetic tree, phylogenetic network, tree-based network, universal tree-based network