# Tail bounds for the height and width of a random tree with a given degree sequence

@article{AddarioBerry2012TailBF,
title={Tail bounds for the height and width of a random tree with a given degree sequence},
journal={Random Struct. Algorithms},
year={2012},
volume={41},
pages={253-261}
}
• Published 2012
• Mathematics, Computer Science
• Random Struct. Algorithms
• Fix a sequence c = (c1,…,cn) of non-negative integers with sum n − 1. We say a rooted tree T has child sequence c if it is possible to order the nodes of T as v1,…,vn so that for each 1 ≤ i ≤ n, vi has exactly ci children. Let \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}${\mathcal T}$\end{document} **image** be a plane tree drawn uniformly at random from among all plane trees with child sequence c. In this note we prove sub-Gaussian tail… CONTINUE READING
14 Citations

#### References

SHOWING 1-10 OF 12 REFERENCES
The Distribution of Heights of Binary Trees and Other Simple Trees
• Mathematics, Computer Science
• Comb. Probab. Comput.
• 1993
• 45
• PDF
The Phase Transition in the Configuration Model
• O. Riordan
• Mathematics, Computer Science
• Comb. Probab. Comput.
• 2012
• 64
• PDF
Concentration
• 469
• Highly Influential
• PDF
Counting labelled trees
• 333
• PDF
The component sizes of a critical random graph with a given degree sequence, arXiv:1012.2352v2 [math.PR
• 2011