On the diameter of the rotation graph of binary coupling trees Review Article

A binary coupling tree on n+1 leaves is a binary tree in which the leaves have distinct labels. The rotation graph Gn is defined as the graph of all binary coupling trees on n+1 leaves, with edges connecting trees that can be transformed into each other by a single rotation. In this paper, we study distance properties of the graph Gn. Exact results for the diameter of Gn for values up to n=10 are obtained. For larger values of n, we prove upper and lower bounds for the diameter, which yield the result that the diameter of Gn grows like n lg(n).