# Dynamic monopolies and degenerate sets

Dynamic monopolies are a widely studied model for influence diffusion in social networks. For a graph $G$ and an integer-valued threshold function $\tau$ on its vertex set, a dynamic monopoly is a set of vertices of $G$ such that iteratively adding to it vertices $u$ of $G$ that have at least $\tau(u)$ neighbours in it eventually yields the entire vertex set of $G$.

I present recent bounds, algorithms, and hardness results for minimum dynamic monopolies and its dual problem of maximum degenerate sets.

Some parts are joint work with S. Bessy, C. Brause, L.D. Penso, and D. Rautenbach.

This talk is part of the Combinatorics and Probability Seminar series.