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#### Article Title

An Eternal Domination Problem in Grids

#### Abstract

A dynamic domination problem in graphs is considered in which an infinite sequence of attacks occur at vertices with mobile guards; the guard at the attacked vertex is required to vacate the vertex by moving to a neighboring vertex with no guard. Other guards are allowed to move at the same time, and before and after each attack, the vertices containing guards must form a dominating set of the graph. The minimum number of guards that can defend the graph against such an arbitrary sequence of attacks is called the m-eviction number of the graph. In this paper, the m-eviction number is determined exactly for $m \times n$ grids with $m \leq 4$ and upper bounds are given for all $n \geq m \geq 8$.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

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Supplemental Reference List with DOIs

COinS

#### DOI

https://doi.org/10.20429/tag.2017.040102