Trees of Diameter 4

Abstract

We will consider plane connected trees up to the isotopy equivalence: two trees are isotopically equivalent, if there exists a continuous orientation preserving deformation of the plane that maps one tree into another. We assume that each tree has a given binary structure, i.e. a coloring of vertices in two colors black and white, such that adjacent vertices have different colors. A type is a (finite) set of all trees, which have the same sets of valences of black and white vertices. If k ₁, ... , k _s is the set of valences of white vertices and l ₁, ... , l _t is the set of valences of black vertices, then the corresponding type is denoted as 〈k ₁, ... , k _s; l ₁ ... , l _s〉.