Georgia Institute of Technology College of Sciences

The notion of weak saturation was introduced by Bollobás in 1968. A graph $G$ on $n$ vertices is weakly $F$-saturated if the edges of $E(K_n) \setminus  E(G)$ can be added to $G$, one edge at a time, in such a way that every added edge creates a new copy of $F$. The minimum size of a weakly $F$-saturated graph $G$ of order $n$ is denoted by $\mathrm{wsat}(n, F)$. In this talk, we discuss the weak saturation number of complete bipartite graphs and determine $\mathrm{wsat}(n, K_{t,t})$ whenever $n > 3t-4$. For fixed $1