Almost all trees have tribe number 2 or 3
For a fixed \(\varepsilon\leq 1/2\), the tribe number \(t_T(\varepsilon)\) of \(T\) is defined as the smallest integer \(r\), such that for every vertex \(v\) in \(T\), the forest obtained from deleting \(v\) from \(T\) contains a collection of at most \(r\) trees that contain together more than \((1- \varepsilon)n\) vertices (\(n\) denoting the number of vertices of \(T\)). The tribe number of a tree can be arbitrarily large. However, as is shown in this paper, almost every tree has tribe number 2 or 3 (with respect to any fixed \(\varepsilon\leq 1/2\)).
scientific article; zbMATH DE number 790561