Tight universal bounds on the height times the width of random trees

Serte Donderwinkel; Robin Khanfir

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arXiv · 2501.00458

Tight universal bounds on the height times the width of random trees

Serte Donderwinkel·Robin Khanfir

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Abstract

We obtain assumption-free, non-asymptotic, uniform bounds on the product of the height and the width of uniformly random trees with a given degree sequence, conditioned Bienaym\'e trees and simply generated trees. We show that for a tree of size $n$, this product is $O(n \log n)$ in probability, answering a question by Addario-Berry (2019). The order of this bound is tight in this generality.

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Serte Donderwinkel, Robin Khanfir. 2024-12-31. Tight universal bounds on the height times the width of random trees. https://arxiv.org/abs/2501.00458

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