Almost all trees have tribe number 2 or 3

Let T be a tree on n vertices, and let ε ⩽ 12 be a small fixed positive number. The tribe number tT(ϵ) of T is the smallest integer r such that when any vertex is deleted, some r or fewer subtrees in the resulting forest together contain more than (1−ε)n vertices. We prove the following, theorem: Almost all trees have tribe number 2 or 3.