On a Nonuniform Random Recursive Tree

Abstract

This chapter discusses a nonuniform random recursive tree. A tree is a connected graph which has no cycles. Tree R with n vertices labelled 1, 2, …, n is a recursive tree if for each k such that 2≤ k≤n the labels of vertices in the unique path from the first vertex to the kth vertex of a tree form an increasing subsequence of {1,2, . . ., n}. A random recursive tree with n vertices (n-RRT) is a tree picked at random from the family of all recursive trees with n vertices. The chapter deals with a random recursive tree such that the probability of joining a new vertex to the vertex i depends only on the degree of vertex i. In addition, the chapter considers two special cases of the random recursive tree.