The Brush Number of the Two-Dimensional Torus
Combinatorics
2010-12-22 v1
Abstract
In this paper we are interested in the brush number of a graph - a concept introduced by McKeil and by Messinger, Nowakowski and Pralat. Our main aim in this paper is to determine the brush number of the two-dimensional torus. This answers a question of Bonato and Messinger. We also find the brush number of the cartesian product of a clique with a path, which is related to the Box Cleaning Conjecture of Bonato and Messinger.
Keywords
Cite
@article{arxiv.1012.4634,
title = {The Brush Number of the Two-Dimensional Torus},
author = {Ta Sheng Tan},
journal= {arXiv preprint arXiv:1012.4634},
year = {2010}
}