English

On the Minimum Size of a Contraction-Universal Tree

Discrete Mathematics 2009-11-17 v1

Abstract

A tree T_uni is m-universal for the class of trees if for every tree T of size m, T can be obtained from T_uni by successive contractions of edges. We prove that a m-universal tree for the class of trees has at least mln(m) + (gamma-1)m + O(1) edges where is the Euler's constant and we build such a tree with less than mc edges for a fixed constant c = 1.984...

Cite

@article{arxiv.0911.2807,
  title  = {On the Minimum Size of a Contraction-Universal Tree},
  author = {Olivier Bodini},
  journal= {arXiv preprint arXiv:0911.2807},
  year   = {2009}
}
R2 v1 2026-06-21T14:11:40.346Z