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}
}