New Upper Bounds on the Distance Domination Numbers of Grids
Abstract
In his 1992 Ph.D. thesis Chang identified an efficient way to dominate grid graphs and conjectured that his construction gives the most efficient dominating sets for relatively large grids. In 2011 Gon\c{c}alves, Pinlou, Rao, and Thomass\'e proved Chang's conjecture, establishing a closed formula for the domination number of a grid. In March 2013 Fata, Smith and Sundaram established upper bounds for the -distance domination numbers of grid graphs by generalizing Chang's construction of dominating sets to -distance dominating sets. In this paper we improve the upper bounds established by Fata, Smith, and Sundaram for the -distance domination numbers of grids.
Cite
@article{arxiv.1410.4149,
title = {New Upper Bounds on the Distance Domination Numbers of Grids},
author = {Armando Grez and Michael Farina},
journal= {arXiv preprint arXiv:1410.4149},
year = {2014}
}
Comments
12 pages, 9 figures, paper presented at USTARS 2014. arXiv admin note: text overlap with arXiv:1401.2499 by other authors