A note on the independence number, domination number and related parameters of random binary search trees and random recursive trees

TL;DR

This paper analyzes the asymptotic behavior of the independence and domination numbers in random binary search trees and recursive trees, establishing their mean growth and normal fluctuation laws using a recent fringe tree theorem.

Contribution

It applies a new general fringe tree theorem to derive the mean growth and fluctuation laws for independence and domination numbers in two types of random trees.

Findings

Mean growth rates of independence and domination numbers identified.

Normal fluctuation laws established for these parameters.

Results demonstrate the applicability of fringe tree theorems to complex tree parameters.

Abstract

We identify the mean growth of the independence number of random binary search trees and random recursive trees and show normal fluctuations around their means. Similarly we also show normal limit laws for the domination number and variations of it for these two cases of random tree models. Our results are an application of a recent general theorem of Holmgren and Janson on fringe trees in these two random tree models.