Weak saturation numbers of complete bipartite graphs in the clique

The notion of weak saturation was introduced by Bollobás in 1968. Let F and H be graphs. A spanning subgraph G⊆F is weakly(F,H)-saturated if it contains no copy of H but there exists an ordering e1,…,et of E(F)∖E(G) such that for each i∈[t], the graph G∪{e1,…,ei} contains a copy H′ of H such that ei∈H′. Define wsat(F,H) to be the minimum number of edges in a weakly (F,H)-saturated graph. In this paper, we prove for all t≥2 and n≥3t−3, that wsat(Kn,Kt,t)=(t−1)(n+1−t/2), and we determine the value of wsat(Kn,Kt−1,t) as well. For fixed 2≤s