Closing the Gap: Eternal Domination on 3 x n Grids

Authors

  • Margaret-Ellen Messinger Mount Allison University

DOI:

https://doi.org/10.11575/cdm.v12i1.62531

Keywords:

graph protection, all guards move, m-eternal domination

Abstract

The domination number for grid graphs has been a long studied problem; the first results appeared over thirty years ago [Jacobson 1984] and the final results appeared in 2013 [Goncalves 2013]. Grid graphs are a natural class of graphs to consider for the eternal dominating set problem as the domination number forms a lower bound for the eternal domination number.  The 3 x n grid has been considered in several papers, and the difference between the upper and lower bounds for the eternal domination number in the all-guards move model has been reduced to a linear function of n. In this short paper, we provide an upper bound for the eternal domination number which exceeds the lower bound by at most 3.

References

References

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Published

2017-09-27

Issue

Vol. 12 No. 1 (2017)

Section

Articles

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