English

The Domination Number of Grids

Discrete Mathematics 2014-01-20 v1

Abstract

In this paper, we conclude the calculation of the domination number of all n×mn\times m grid graphs. Indeed, we prove Chang's conjecture saying that for every 16nm16\le n\le m, γ(Gn,m)=(n+2)(m+2)54\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4.

Keywords

Cite

@article{arxiv.1102.5206,
  title  = {The Domination Number of Grids},
  author = {Daniel Gonçalves and Alexandre Pinlou and Michael Rao and Stéphan Thomassé},
  journal= {arXiv preprint arXiv:1102.5206},
  year   = {2014}
}

Comments

12 pages, 4 figures