## PIMS-UVic Discrete Math Seminar: Virgelot Virgile

- Date: 09/14/2023
- Time: 10:00

University of Victoria

Recent progress on the eternal eviction game

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.

**Location**: Clearihue C111

**Time**: 10am PacificĀ