In the eternal eviction game, a set of guards placed on the vertices of (a dominating set of) a graph G must move to defend the graph against attacks on those of its vertices that contain guards, while maintaining a dominating set of G. The eternal eviction number of G is the minimum number of guards required to defend G against any sequence of attacks. In this talk, we will present some recent progress on the game. In particular, we will show that for any integer $k \geq 1$, there exists $f(k)$ such that any graph with independence number at most $k$ has eviction number at most $f(k)$.
This is joint work with Gary MacGillivray and Kieka Mynhardt.