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The number of trees with large diameter

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Tomasz Łuczak
Tomasz Łuczak
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland
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Abstract

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In the paper we study the asymptotic behaviour of the number of trees with n vertices and diameter k = k(n), where k/√n → ∞ as n → ∞ but k = o(n).

MSC classification

Secondary: 05C30: Enumeration in graph theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 3 , June 1995 , pp. 298 - 311
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Pavlov, Yu. L., ‘A case of limit distribution of the maximal volume on a tree in a random forest’, Math. Notes 25 (1979), 387–392.CrossRefGoogle Scholar
[2]Rényi, A. and Szekeres, G., ‘On the height of trees’, J. Austral. Math. Soc. (Series A) 7 (1967), 497–507.CrossRefGoogle Scholar
[3]Szekeres, G., ‘Distribution of labelled trees by diameter’, in: Combinatorial Mathematics X, Proc. Conf Adelaide, Australia 1982, Lecture Notes in Math. 1036 (Springer, Berlin, 1983) pp. 392–397.Google Scholar