On Obstacle Numbers
Combinatorics
2013-08-21 v1 Computational Geometry
Discrete Mathematics
Abstract
The obstacle number is a new graph parameter introduced by Alpert, Koch, and Laison (2010). Mukkamala etal (2012) show that there exist graphs with n vertices having obstacle number in Omega(n/\log n). In this note, we up this lower bound to Omega(n/(\log\log n)^2. Our proof makes use of an upper bound of Mukkamala etal on the number of graphs having obstacle number at most h in such a way that any subsequent improvements to their upper bound will improve our lower bound.
Cite
@article{arxiv.1308.4321,
title = {On Obstacle Numbers},
author = {Vida Dujmović and Pat Morin},
journal= {arXiv preprint arXiv:1308.4321},
year = {2013}
}