Identifying \(X\)-trees with few characters (Q869997)

Summary: Previous work has shown the perhaps surprising result that, for any binary phylogenetic tree \(T\), there is a set of four characters that defines \(T\). Here we deal with the general case, where \(T\) is an arbitrary X-tree. We show that if \(d\) is the maximum degree of any vertex in \(T\), then the minimum number of characters that identify \(T\) is \(\log_2 d\) (up to a small multiplicative constant).