Dynamic Monopolies for Degree Proportional Thresholds in Connected Graphs of Girth at least Five and Trees

Michael Gentner, Dieter Rautenbach

Let $G$ be a graph, and let $\rho \in (0,1)$. For a set $D$ of vertices of $G$, let the set $H_{\rho }(D)$ arise by starting with the set $D$, and iteratively adding further vertices $u$ to…