Cutting down very simple trees

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.

Keywords: simply generated trees, cutting down procedure, limiting distribution

Quaestiones Mathematicae 29(2006), 211–227.