We show that for any two values α,β>0 for which
α+β>1 then there is a value N so that for all n≥N the
following holds. For any binary phylogenetic tree T on n leaves there is a
set of ⌊nα⌋ characters that capture T, and for which
each character takes at most ⌊nβ⌋ distinct states. Here
`capture' means that T is the unique perfect phylogeny for these characters.
Our short proof of this combinatorial result is based on the probabilistic
method.Comment: 3 pages, 0 figure