The distribution of nodes of given degree in random trees

Authors:
Michael Drmota;Bernhard Gittenberger
Affiliations:
Institut Für Geometrie, Tu Wien, Wiedner Hauptstrasse 8-10-113, A-1040 Wien, Austria;Institut Für Geometrie, Tu Wien, Wiedner Hauptstrasse 8-10-113, A-1040 Wien, Austria
Venue:
Journal of Graph Theory
Year:
1999

Citing 0
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Abstract

Let Tn denote the set of unrootedunlabeled trees of size n and let k ≥ 1 be given.By assuming that every tree of Tn isequally likely, it is shown that the limiting distribution of thenumber of nodes of degree k is normal with mean value~μkn and variance~σ[stack2k] n withpositive constants μk andσk. Besides, the asymptotic behavior ofμk and σk for k➝ ∞ as well as the corresponding multivariatedistributions are derived. Furthermore, similar results can beproved for plane trees, for labeled trees, and for forests. ©1999 John Wiley & Sons, Inc. J Graph Theory 31: 227253,1999