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Isolating a Leaf in Rooted Trees via Random Cuttings
Markus Kuba and Alois Panholzer
Institut für Diskrete Mathematik und Geometrie, Technische UniversitätWien,Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria
{Markus.Kuba, Alois.Panholzer}@tuwien.ac.at
Annals of Combinatorics 12 (1) p.81-99 March, 2008
AMS Subject Classification:05C05, 05A16, 60F05
Abstract:
We consider a recursive procedure for destroying rooted trees and isolating a leaf by removing a random edge and keeping the subtree, which does not contain the original root. For two tree families, the simply generated tree families and increasing tree families, we study here the number of random cuts that are necessary to isolate a leaf. We can show limiting distribution results of this parameter for simply generated trees and certain increasing trees.
Keywords: simply generated trees, recursive trees, cutting-down procedure, node isolation, limiting distribution

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