title: 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.
authors.affiliation: Department of Statistical Science, School of Multidisciplinary Sciences, SOKENDAI (The Graduate University for Advanced Studies), Tokyo 190-8562, Japan; The Institute of Statistical Mathematics, Tokyo 190-8562, Japan. Electronic address: hayamizu@ism.ac.jp.
authors.forename: Momoko
authors.initials: M
authors.lastname: Hayamizu
mesh_terms: D008962:Models, Theoretical
keywords: Reticulate evolution; binary phylogenetic network; tree-based network