New Upper Bounds on the Distance Domination Numbers of Grids

Abstract

In his 1992 Ph.D. thesis Chang identified an efficient way to dominate $m\times n$ grid graphs and conjectured that his construction gives the most efficient dominating sets for relatively large grids. In 2011 Gonçalves, Pinlou, Rao, and Thomassé 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 $k$-distance domination numbers of grid graphs by generalizing Chang's construction of dominating sets to $k$-distance dominating sets. In this paper we improve the upper bounds established by Fata, Smith, and Sundaram for the $k$-distance domination numbers of grids.

12 pages, 9 figures, paper presented at USTARS 2014. arXiv admin note: text overlap with arXiv:1401.2499 by other authors

References in corpus (1)

• Distributed Dominating Sets on Grids