On the existence of infinitely many universal tree-based networks

Abstract

A tree-based network on a set $X$ of $n$ leaves is said to be universal if any rooted binary phylogenetic tree on $X$ can be its base tree. Francis and Steel showed that there is a universal tree-based network on $X$ in the case of $n=3$, and asked whether such a network exists in general. We settle this problem by proving that there are infinitely many universal tree-based networks for any $n>1$.

4 pages, 2 figures, accepted for publication in Journal of Theoretical Biology. (v1 -> v2: Updates have been made to the author list, Fig 1 caption, Comments, and Acknowledgement; a new paragraph has also been added at the end.)

References in corpus (1)

• On Tree Based Phylogenetic Networks

Cited by in corpus (2)

• Tree-based unrooted phylogenetic networks
• On Determining if Tree-based Networks Contain Fixed Trees