The proportion of trees that are linear

We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on n vertices, characterize the asymptotic growth rate of the number of nonisomorph...

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Bibliographic Details
Published in:Discrete mathematics 2020-10, Vol.343 (10), p.112008, Article 112008
Main Authors: Wakhare, Tanay, Wityk, Eric, Johnson, Charles R.
Format: Article
Language:English
Subjects:
Caterpillars
Linear trees
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Summary:We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on n vertices, characterize the asymptotic growth rate of the number of nonisomorphic linear trees, and show that the distribution of k-linear trees on n vertices follows a central limit theorem.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.112008