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Quaestiones Mathematicae 2006, 29 (2) : 211–227
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Cutting down very simple trees
Authors:
A Panholzer
Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/104, A-1040 Wien, Austria
Corresponding Author: A Panholzer (E-mail: Alois.Panholzer@tuwien.ac.at)
Abstract:
We study here, by using a recursive approach, the number of random cuts that are necessary to destroy a random tree of size n for simply generated tree families. Crucial for the applicability of such a recursive approach is a “randomnesspreservation” property when cutting off a random edge. We can fully characterize the subclass of simply generated tree families, which satisfy this property and show then for for all these tree families that the number of random cuts to destroy a random size-n tree is asymptotically, for n→ ∞, Rayleigh distributed.
Quaestiones Mathematicae 29(2006), 211–227
Keywords: simply generated trees; cutting down procedure; limiting distribution
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