Subtrees of a random tree
Bogumil Kaminski, Pawel Pralat

TL;DR
This paper investigates the asymptotic number of subtrees in a uniformly random labeled tree, providing bounds and computational evidence suggesting a precise exponential growth rate.
Contribution
It establishes bounds for the number of subtrees in random labeled trees and offers computational evidence for a tight asymptotic estimate.
Findings
Bounds for c(n) between 1.41805386^n and 1.41959881^n
Strong computational indication that c(n) ≤ 1.41806183^n
Asymptotic exponential growth rate of subtrees in random trees
Abstract
Let be a random tree taken uniformly at random from the family of labelled trees on vertices. In this note, we provide bounds for , the number of sub-trees of that hold asymptotically almost surely. With computer support we show that . Moreover, there is a strong indication that, in fact, .
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