English

The Proportion of Trees that are Linear

Combinatorics 2020-03-23 v2

Abstract

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 nn vertices, characterize the asymptotic growth rate of the number of nonisomorphic linear trees, and show that the distribution of kk-linear trees on nn vertices follows a central limit theorem.

Keywords

Cite

@article{arxiv.1901.08502,
  title  = {The Proportion of Trees that are Linear},
  author = {Tanay Wakhare and Eric Wityk and Charles R. Johnson},
  journal= {arXiv preprint arXiv:1901.08502},
  year   = {2020}
}

Comments

8 pages; v2 contains new central limit theorem, as suggested by the referee

R2 v1 2026-06-23T07:21:22.312Z