  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 $n>1$.
