2010/12/21 by Ta Sheng Tan, Tan, Ta Sheng · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.1012.4634
arxiv created 2010/12/21 · openalex publication_date 2010/12/21 · arxiv updated 2010/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.