Minimum Contagious Sets in Trees with Degree-Proportional Thresholds

We investigate how large the minimum size of a contagious set can be among trees of a fixed order. Given a graph $G$ and $ρ\in[0,1]$, an inactive vertex $u$ becomes active when at least $\lceil{ρd_G(u)\rceil}$ of its neighbors are active. An initial set of active vertices is contagious if the proc